Use the equation to find the x and y-intercepts:, №17887388, 08.07.2021 13:36

Mathematics

Use the equation to find the x and y-intercepts: 2x + 4y = 12 x-intercept: y-intercept:

Step-by-step answer

P Answered by PhD

1

List the intersections.

x-intercept(s): (6,0)

y-intercept(s): (0,3)

Step-by-step explanation:

Use the equation to find the x and y-intercepts:
2x + 4y = 12
x-intercept:
y-intercept:

Mathematics

1. write the equation in slope-intercept form. identify the slope and y-intercept. show all work 2x - 3y = 9 2. write the equation in slope-intercept form. identify the slope and y-intercept. show all work x - 4y = -20 3. find the x- and y-intercepts for -x + 4y = 12. write each intercept as a unique ordered pair. show all work 4. y = 2/3x + 7 written in standard form using integers is 3x - y = 21. a) true b) false 5. write an equation of a line that has the same slope as 2x – 5y = 12 and the same y-intercept as 4y + 24 = 5x. a) y= 2/5x−6 b) y=6x−2/5

Step-by-step answer

P Answered by PhD

46

Part 1)

we know that

the equation of the line in slope-intercept form is equal to

y=mx+b

where

m is the slope

b is the y-intercept

we have

2x-3y=9

solve for y

3y=2x-9

y=(2/3)x-3 -------> equation of the line in slope-intercept form

so

the slope m is $\frac{2}{3}$

the y-intercept b is

Part 2)

we know that

the equation of the line in slope-intercept form is equal to

y=mx+b

where

m is the slope

b is the y-intercept

we have

x-4y=-20

solve for y

4y=x+20

y=(1/4)x+5 -------> equation of the line in slope-intercept form

so

the slope m is $\frac{1}{4}$

the y-intercept b is

Part 3)

we know that

The x-intercept is the value of x when the value of y is equal to zero

The y-intercept is the value of y when the value of x is equal to zero

we have

-x+4y=12

a) Find the x-intercept

For y=0 substitute in the equation

-x+4*0=12

x=-12

The answer part 3a) is (-12,0)

b) Find the y-intercept

For x=0 substitute in the equation

-0+4y=12

y=3

The answer part 3b) is (0,3)

Part 4)

we know that

the equation of the line in standard form is

Ax+By=C

we have

$y=\frac{2}{3}x+7$

Multiply by both sides

3y=2x+21

2x-3y=-21 ------> equation in standard form

therefore

the answer Part 4) is option B False

Part 5)

Step 1

Find the slope

we have

2x-5y=12

solve for y

5y=2x-12

y=(2/5)x-(12/5)

so

the slope m is $\frac{2}{5}$

Step 2

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

we have

4y+24=5x

for x=0

4y+24=5*0

4y=-24

y=-6

the y-intercept is

Step 3

Find the equation of the line

we have

$m=\frac{2}{5}$

b=-6

the equation of the line in slope-intercept form is

y=mx+b

substitute the values

$y=\frac{2}{5}x-6$

therefore

the answer Part 5) is the option A $y=\frac{2}{5}x-6$

Part 6)

Step 1

Find the slope of the given line

we know that

if two lines are perpendicular. then the product of their slopes is equal to minus one

so

m1*m2=-1

in this problem

the given line

x+8y=27

solve for y

8y=27-x

y=(27/8)-(x/8)

the slope m1 is $m1=-\frac{1}{8}$

so

the slope m2 is m2=8

Step 2

Find the equation of the line

we know that

the equation of the line in slope point form is equal to

y-y1=m*(x-x1)

we have

m2=8

point (-5,5)

substitutes the values

y-5=8*(x+5)

y=8x+40+5

y=8x+45

therefore

the answer part 6) is the option C y=8x+45

Part 7)

y=(8/3)x+ 19 -------> the slope is m=(8/3)

8x- y=17

y =8x-17 --------> the slope is m=8

we know that

if two lines are parallel , then their slopes are the same

in this problem the slopes are not the same

therefore

the answer part 7) is the option D) No, since the slopes are different.

Part 8)

a. Write an equation for the line in point-slope form

b. Rewrite the equation in standard form using integers

Step 1

Find the slope of the line

we know that

the slope between two points is equal to

$m=\frac{(y2-y1)}{(x2-x1)}$

substitute the values

$m=\frac{(4+1)}{(8-2)}$

$m=\frac{(5)}{(6)}$

Step 2

Find the equation in point slope form

we know that

the equation of the line in slope point form is equal to

y-y1=m*(x-x1)

we have

m=(5/6)

point (2,-1)

substitutes the values

y+1=(5/6)*(x-2) -------> equation of the line in point slope form

Step 3

Rewrite the equation in standard form using integers

y=(5/6)x-(5/3)-1

y=(5/6)x-(8/3)

Multiply by both sides

6y=5x-16

5x-6y=16 --------> equation of the line in standard form

Part 9)

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{(y2-y1)}{(x2-x1)}$

where

(x1,y1) ------> is the first point

(x2,y2) -----> is the second point

In the numerator calculate the difference of the y-coordinates

in the denominator calculate the difference of the x-coordinates

Part 10)

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{(y2-y1)}{(x2-x1)}$

substitutes

$m=\frac{(5+1)}{(-1+3)}$

$m=\frac{(6)}{(2)}$

m=3

therefore

the answer Part 10) is m=3

Part 11)

we know that

the equation of the line in slope point form is equal to

y-y1=m*(x-x1)

substitute the values

y+9=-2*(x-10) --------> this is the equation in the point slope form

Mathematics

Algebra 1a unit 6 lesson 6 1. write an equation in slope-intercept form of the line rhat passes through the given point and is parallele to the graph of the equation (2,-2); y=-x-2 2. (2,-1); y=-3/2x+6 3. (4,2); x=-3 4. (-2,3); y=1/2x-1 5. (5,0); y+1=2(x-3) 6. determine whether the graphs of the given equations are parellel, perpendicular, or neither y=x+11 y=-x+2 7. y=-2x+3 y=2x+y=7 8. y=4x-2 -x+4y=0 9. determine whether the statement is always, sometimes or never true two lines with positive slopes are parellel 10. two lines with the same slope

Step-by-step answer

P Answered by PhD

21

1. y = -x - 2...slope here is -1. A parallel line will have the same slope

y = mx + b
slope(m) = -1
(2,-2)...x = 2 and y = -2
now we sub and find b, the y int
-2 = -1(2) + b
-2 = -2 + b
-2 + 2 = b
0 = b

so ur parallel equation is : y = -x

2. -1 = -3/2(2) + b
-1 = -3 + b
-1 + 3 = b
2 = b
parallel equation is : y = -3/2x + 2

3. parallel equation is : x = 4

4. 3 = 1/2(-2) + b
3 = -1 + b
3 + 1 = b
4 = b
parallel equation is : y = 1/2x + 4

5. y + 0 = 2(x - 5)
y = 2x - 10 <== parallel line

6. neither

7. if ur second equation is : 2x + y = 7, then the lines are parallel

8. neither

9. sometimes

10. never

Mathematics

A) Find the coordinates of the points of intersection of the graphs with coordinate axes: b y=−2x+4 B) Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes. c 2x+3y=6 C)Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes. d 1.2x+2.4y=4.8 can you please help me i will give you brainily

Step-by-step answer

P Answered by PhD

Step-by-step explanation:

A)

y=−2x+4

y-int:

y=−2*0+4

y=4

x-int:

0=−2x+4

2x=4

x=2

(2,4)

B)

2x+3y=6

y-int:

2*0+3y=6

3y=6

y=2

x-int:

2x+3*0=6

2x=6

x=3

(3,2)

C)

1.2x+2.4y=4.8

y-int:

1.2*0+2.4y=4.8

2.4y=4.8

24y=48

y=2

x-int:

1.2x+2.4*0=4.8

1.2x=4.8

12x=48

x=4

(4,2)

Mathematics

Algebra 1a unit 6 lesson 6 1. write an equation in slope-intercept form of the line rhat passes through the given point and is parallele to the graph of the equation (2,-2); y=-x-2 2. (2,-1); y=-3/2x+6 3. (4,2); x=-3 4. (-2,3); y=1/2x-1 5. (5,0); y+1=2(x-3) 6. determine whether the graphs of the given equations are parellel, perpendicular, or neither y=x+11 y=-x+2 7. y=-2x+3 y=2x+y=7 8. y=4x-2 -x+4y=0 9. determine whether the statement is always, sometimes or never true two lines with positive slopes are parellel 10. two lines with the same slope

Step-by-step answer

P Answered by PhD

21

1. y = -x - 2...slope here is -1. A parallel line will have the same slope

y = mx + b
slope(m) = -1
(2,-2)...x = 2 and y = -2
now we sub and find b, the y int
-2 = -1(2) + b
-2 = -2 + b
-2 + 2 = b
0 = b

so ur parallel equation is : y = -x

2. -1 = -3/2(2) + b
-1 = -3 + b
-1 + 3 = b
2 = b
parallel equation is : y = -3/2x + 2

3. parallel equation is : x = 4

4. 3 = 1/2(-2) + b
3 = -1 + b
3 + 1 = b
4 = b
parallel equation is : y = 1/2x + 4

5. y + 0 = 2(x - 5)
y = 2x - 10 <== parallel line

6. neither

7. if ur second equation is : 2x + y = 7, then the lines are parallel

8. neither

9. sometimes

10. never

Mathematics

Find x- and y-intercepts. write ordered pairs representing the points where the line crosses the axes. 1. y=5x−10 2. y=2x−3 3. x+4y=12 4. x−y=4 5. y=−2x 6. y−4x=0 7. 0.3x−0.4y=0.7 8. y= 2/3 x− 1/3

Step-by-step answer

P Answered by Specialist

5

1. y=5x-10

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

y=5x-10

0=5x-10

10=5x

∴ x=2

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

y=5x-10

y=5(0)-10

y=0-10 =

∴ y=-10.

The ordered pairs representing the points where the line y=5x-10 crosses the axes are, (2,0) and (0, -10) .

2. y=2x-3

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

y=2x-3

0=2x-3

3=2x

∴ $x=\frac{3}{2}$

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

y=2x-3

y=2(0)-3

y=0-3 =

∴ y=-3.

The ordered pairs representing the points where the line y=2x-3 crosses the axes are, $(\frac{3}{2} ,0)$ and (0, -3) .

3. x+4y=12

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

x+4y=12

$x+4\cdot (0)=12$

x+0=12

∴ x=12

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

x+4y=12

0+4y=12

4y=12

∴ y=3.

The ordered pairs representing the points where the line x+4y=12 crosses the axes are, (12, 0) and (0, 3) .

4. x-y=4

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

x-y=4

x-0=4

∴ x=4

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

x-y=4

0-y=4

y=-4

∴ y=-4.

The ordered pairs representing the points where the line x-y=4 crosses the axes are, (4, 0) and (0, -4) .

5. y=-2x

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

y=-2x

0=-2x

∴ x=0

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

$y=-2\cdot(0)$

y=0

∴ y=0.

The ordered pairs representing the points where the line y=-2x crosses the axes is, (0, 0)

6. y-4x=0

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

y-4x=0

0-4x=0

-4x=0

∴ x=0

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

y-4x=0

$y-4\cdot (0)=0$

y-0=0

∴ y=0.

The ordered pairs representing the points where the line y-4x=0 crosses the axes is, (0,0)

7. 0.3x-0.4y=0.7

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

$0.3x-0.4\cdot (0)=0.7$

0.3x-0=0.7

$x=\frac{0.7}{0.3}$

∴ $x=\frac{7}{3}$

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

$0.3\cdot(0)-0.4y=0.7$

0-0.4y=0.7

-0.4y=0.7

$y=-\frac{0.7}{0.4}$

∴ $y=-\frac{7}{4}$

The ordered pairs representing the points where the line 0.3x-0.4y=0.7 crosses the axes are, $(\frac{7}{3} , 0)$ and $(0, -\frac{7}{4} )$ .

8. $y=\frac{2}{3}x-\frac{1}{3}$

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

$0=\frac{2}{3}x-\frac{1}{3}$

$\frac{2}{3}x=\frac{1}{3}$

$x=\frac{1}{3}\cdot \frac{3}{2}$

∴ $x=\frac{1}{2}$

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

$y=\frac{2}{3}\cdot (0)-\frac{1}{3}$

$y=0-\frac{1}{3}$

∴ $y=-\frac{1}{3}$

The ordered pairs representing the points where the line $y=\frac{2}{3}x-\frac{1}{3}$ crosses the axes are, $(\frac{1}{2}, 0)$ and $(0, -\frac{1}{3} )$

Mathematics

Find x- and y-intercepts. write ordered pairs representing the points where the line crosses the axes. 1. y=5x−10 2. y=2x−3 3. x+4y=12 4. x−y=4 5. y=−2x 6. y−4x=0 7. 0.3x−0.4y=0.7 8. y= 2/3 x− 1/3

Step-by-step answer

P Answered by Master

5

1. y=5x-10

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

y=5x-10

0=5x-10

10=5x

∴ x=2

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

y=5x-10

y=5(0)-10

y=0-10 =

∴ y=-10.

The ordered pairs representing the points where the line y=5x-10 crosses the axes are, (2,0) and (0, -10) .

2. y=2x-3

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

y=2x-3

0=2x-3

3=2x

∴ $x=\frac{3}{2}$

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

y=2x-3

y=2(0)-3

y=0-3 =

∴ y=-3.

The ordered pairs representing the points where the line y=2x-3 crosses the axes are, $(\frac{3}{2} ,0)$ and (0, -3) .

3. x+4y=12

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

x+4y=12

$x+4\cdot (0)=12$

x+0=12

∴ x=12

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

x+4y=12

0+4y=12

4y=12

∴ y=3.

The ordered pairs representing the points where the line x+4y=12 crosses the axes are, (12, 0) and (0, 3) .

4. x-y=4

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

x-y=4

x-0=4

∴ x=4

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

x-y=4

0-y=4

y=-4

∴ y=-4.

The ordered pairs representing the points where the line x-y=4 crosses the axes are, (4, 0) and (0, -4) .

5. y=-2x

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

y=-2x

0=-2x

∴ x=0

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

$y=-2\cdot(0)$

y=0

∴ y=0.

The ordered pairs representing the points where the line y=-2x crosses the axes is, (0, 0)

6. y-4x=0

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

y-4x=0

0-4x=0

-4x=0

∴ x=0

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

y-4x=0

$y-4\cdot (0)=0$

y-0=0

∴ y=0.

The ordered pairs representing the points where the line y-4x=0 crosses the axes is, (0,0)

7. 0.3x-0.4y=0.7

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

$0.3x-0.4\cdot (0)=0.7$

0.3x-0=0.7

$x=\frac{0.7}{0.3}$

∴ $x=\frac{7}{3}$

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

$0.3\cdot(0)-0.4y=0.7$

0-0.4y=0.7

-0.4y=0.7

$y=-\frac{0.7}{0.4}$

∴ $y=-\frac{7}{4}$

The ordered pairs representing the points where the line 0.3x-0.4y=0.7 crosses the axes are, $(\frac{7}{3} , 0)$ and $(0, -\frac{7}{4} )$ .

8. $y=\frac{2}{3}x-\frac{1}{3}$

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

$0=\frac{2}{3}x-\frac{1}{3}$

$\frac{2}{3}x=\frac{1}{3}$

$x=\frac{1}{3}\cdot \frac{3}{2}$

∴ $x=\frac{1}{2}$

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

$y=\frac{2}{3}\cdot (0)-\frac{1}{3}$

$y=0-\frac{1}{3}$

∴ $y=-\frac{1}{3}$

The ordered pairs representing the points where the line $y=\frac{2}{3}x-\frac{1}{3}$ crosses the axes are, $(\frac{1}{2}, 0)$ and $(0, -\frac{1}{3} )$

Mathematics

Given the following system of equations and its graph below, what can be determined about the slopes and y-intercepts of the system of equations? A line includes points 0 comma 4 and 2 comma 3. A line includes points 0 comma 3 and 4 comma 1. x + 2y = 8 2x + 4y = 12 The slopes are different, and the y-intercepts are different. The slopes are different, and the y-intercepts are the same. The slopes are the same, and the y-intercepts are different. The slopes are the same, and the y-intercepts are the same.

Step-by-step answer

P Answered by PhD

4

The slopes are the same, and the y-intercepts are different

Step-by-step explanation:

To find the slope of each equation, we first need to rewrite the equations isolating y. So, we have that:

First equation:

x + 2y = 8

2y = 8 - x

y = -0.5x + 4

Second equation:

2x + 4y = 12

x + 2y = 6

2y = 6 - x

y = -0.5x + 3

The slope is the coefficient of x, and they are the same in both equations, so they have the same slope.

The y-intercepts is the constant that is not multiplied by x, so in the first equation it is 4, and in the second it is 3, so the equations don't have the same y-intercepts.

Mathematics

A) Find the coordinates of the points of intersection of the graphs with coordinate axes: b y=−2x+4 B) Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes. c 2x+3y=6 C)Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes. d 1.2x+2.4y=4.8 can you please help me i will give you brainily

Step-by-step answer

P Answered by PhD

Step-by-step explanation:

A)

y=−2x+4

y-int:

y=−2*0+4

y=4

x-int:

0=−2x+4

2x=4

x=2

(2,4)

B)

2x+3y=6

y-int:

2*0+3y=6

3y=6

y=2

x-int:

2x+3*0=6

2x=6

x=3

(3,2)

C)

1.2x+2.4y=4.8

y-int:

1.2*0+2.4y=4.8

2.4y=4.8

24y=48

y=2

x-int:

1.2x+2.4*0=4.8

1.2x=4.8

12x=48

x=4

(4,2)

Mathematics

Given the following system of equations and its graph below, what can be determined about the slopes and y-intercepts of the system of equations? x + 2y = 8 2x + 4y = 12 A) The slopes are different, and the y-intercepts are different. B) The slopes are different, and the y-intercepts are the same. C) The slopes are the same, and the y-intercepts are different. D) The slopes are the same, and the y-intercepts are the same.

Step-by-step answer

P Answered by PhD

7

C) The slopes are the same, and the y-intercepts are different.

Step-by-step explanation:

From the graph we see that they are parallel ( so the slopes are the same) but they have different y-intercepts.

Use the equation to find the x and y-intercepts:
2x + 4y = 12
x-intercept:
y-intercept:

Step-by-step answer

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