What is the equation of the line that passes, №18011123, 25.02.2023 14:16

Mathematics

What is the equation of the line that passes through the point (3,7) and has a slope of 2/3

Step-by-step answer

P Answered by Specialist

$Y=\frac{2}{3} x +5$

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What is the equation of the line that passes through the point (3,7) and has a slope of 2/3

Mathematics

1) Which equation represents the line that passes through the point (3, 10) and has a slope of 3? 2) What is an equation for the line that passes through the coordinates (0, 3) and has a slope of -3/2? 3) Write an equation of the line that passes through the point (–2, 4) with slope 1. 4) What is the equation of the line that passes through the point (3,7) and has a slope of 4/3?

Step-by-step answer

P Answered by Master

14

1

Step-by-step explanation:

Because it is the correct answer

Mathematics

1) Which equation represents the line that passes through the point (3, 10) and has a slope of 3? 2) What is an equation for the line that passes through the coordinates (0, 3) and has a slope of -3/2? 3) Write an equation of the line that passes through the point (–2, 4) with slope 1. 4) What is the equation of the line that passes through the point (3,7) and has a slope of 4/3?

Step-by-step answer

P Answered by Specialist

14

1

Step-by-step explanation:

Because it is the correct answer

Mathematics

Find the distance between (3, 8) and (7, -11). round to the nearest hundredth. find the coordinates of the midpoint of jk if j (-9, 5) and k(21, -7). find the coordinates of the midpoint of ab if a(-8, 7) and b(-9, 11). if the midpoint between (8, y) and (-11, 6) is (-1.5, 5), find the value of y. find the slope of the line that passes through the points (3, -6) and (6, 12). find the value of x so that the line passing through (x, 10) and (-4, 8) has a slope of 2/3 find the value of y so that the line passing through (9, 0) and (3, y) has a slope

Step-by-step answer

P Answered by PhD

3

The answers are;

The distance between (3,8)

and

is $19.42\text{ (to the nearest hundredth)}$ The midpoint of the line

is

The midpoint of the line

is

The value of

is

The slope of the line that passes through $(3,-6)\text{ and }(6,12)$ is

The value of

is

The value of

is $-\frac{3}{2}$ The slope of the line that passes through $(8,7)\text{ and }(11,7)$ is

In coordinate geometry, given two points (x_1,y_1) and (x_2,y_2) ;

The distance between them is given by $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ The midpoint has the coordinates $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ The slope of the line passing through the points is the ratio $\frac{y_2-y_1}{x_2-x_1}$

These formulae will be used to solve the following problems:

1) Given points (3,8) and (7,-11) , the distance between them is

$\sqrt{(7-3)^2+(-11-8)^2}\approx 19.42 \text{ (to the nearest hundredth)}$

2) If $J=(-9,5) \text{ and }K=(21,-7)$ , the midpoint of the line is

$(\frac{-9+21}{2}, \frac{5+(-7)}{2})=(6,-1)$

3) If $A=(-8,7) \text{ and } B=(-9,11)$ , the midpoint of the line is

$(\frac{-8+(-9)}{2}, \frac{7+11}{2})=(8.5,9)$

4) If the midpoint between $(8,y) \text{ and } (-11,6)$ is (-1.5,5) , then, using the

midpoint formula for the y-coordinate

$6=\frac{y+5}{2} \implies y=7$

5) The slope of the line that passes through $(3,-6)\text{ and }(6,12)$ is

$\frac{12-(-6)}{6-3}=6$

6) If the slope of the line that passes through $(x,10)\text{ and }(-4,8)$ is $\frac{2}{3}$ , then,

using the slope formula

$\frac{2}{3}=\frac{8-10}{-4-x}\\\implies \frac{2}{3}=\frac{10-8}{4+x}\\\implies \frac{2}{3}=\frac{2}{4+x}\\\implies x=-1$

7) If the slope of the line that passes through $(9,0)\text{ and }(3,y)$ is $\frac{1}{2}$ , then,

using the slope formula

$\frac{1}{2}=\frac{y-0}{3-9}\\\implies \frac{1}{2}=\frac{y}{-3}\\\implies y=-\frac{3}{2}$

8) The slope of the line that passes through $(8,7)\text{ and }(11,7)$ is

$\frac{7-7}{11-8}=0$ , (since the y-coordinates of both points are equal)

Learn more about gradients here: link

Mathematics

Find the distance between (3, 8) and (7, -11). round to the nearest hundredth. find the coordinates of the midpoint of jk if j (-9, 5) and k(21, -7). find the coordinates of the midpoint of ab if a(-8, 7) and b(-9, 11). if the midpoint between (8, y) and (-11, 6) is (-1.5, 5), find the value of y. find the slope of the line that passes through the points (3, -6) and (6, 12). find the value of x so that the line passing through (x, 10) and (-4, 8) has a slope of 2/3 find the value of y so that the line passing through (9, 0) and (3, y) has a slope

Step-by-step answer

P Answered by PhD

3

The answers are;

The distance between (3,8)

and

is $19.42\text{ (to the nearest hundredth)}$ The midpoint of the line

is

The midpoint of the line

is

The value of

is

The slope of the line that passes through $(3,-6)\text{ and }(6,12)$ is

The value of

is

The value of

is $-\frac{3}{2}$ The slope of the line that passes through $(8,7)\text{ and }(11,7)$ is

In coordinate geometry, given two points (x_1,y_1) and (x_2,y_2) ;

The distance between them is given by $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ The midpoint has the coordinates $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ The slope of the line passing through the points is the ratio $\frac{y_2-y_1}{x_2-x_1}$

These formulae will be used to solve the following problems:

1) Given points (3,8) and (7,-11) , the distance between them is

$\sqrt{(7-3)^2+(-11-8)^2}\approx 19.42 \text{ (to the nearest hundredth)}$

2) If $J=(-9,5) \text{ and }K=(21,-7)$ , the midpoint of the line is

$(\frac{-9+21}{2}, \frac{5+(-7)}{2})=(6,-1)$

3) If $A=(-8,7) \text{ and } B=(-9,11)$ , the midpoint of the line is

$(\frac{-8+(-9)}{2}, \frac{7+11}{2})=(8.5,9)$

4) If the midpoint between $(8,y) \text{ and } (-11,6)$ is (-1.5,5) , then, using the

midpoint formula for the y-coordinate

$6=\frac{y+5}{2} \implies y=7$

5) The slope of the line that passes through $(3,-6)\text{ and }(6,12)$ is

$\frac{12-(-6)}{6-3}=6$

6) If the slope of the line that passes through $(x,10)\text{ and }(-4,8)$ is $\frac{2}{3}$ , then,

using the slope formula

$\frac{2}{3}=\frac{8-10}{-4-x}\\\implies \frac{2}{3}=\frac{10-8}{4+x}\\\implies \frac{2}{3}=\frac{2}{4+x}\\\implies x=-1$

7) If the slope of the line that passes through $(9,0)\text{ and }(3,y)$ is $\frac{1}{2}$ , then,

using the slope formula

$\frac{1}{2}=\frac{y-0}{3-9}\\\implies \frac{1}{2}=\frac{y}{-3}\\\implies y=-\frac{3}{2}$

8) The slope of the line that passes through $(8,7)\text{ and }(11,7)$ is

$\frac{7-7}{11-8}=0$ , (since the y-coordinates of both points are equal)

Learn more about gradients here: link

Mathematics

1. write the standard form of the line that passes through the given points. include your work in your final answer. (3, 1) and (-2, 3) 2. (4, 7) and (0, 7) 3. (2, 3) and (2, 5) 4.write the slope-intercept form of the line with a slope of 2 and a y -intercept of -4. include your work in your final answer. 5. write the standard form of the line that is parallel to 2 x + 3 y = 4 and passes through the point (1, -4). include your work in your final answer. 6. write the standard form of the line that contains a slope of 2/3 and passes through the point

Step-by-step answer

P Answered by PhD

8

Part 1) 2x+5y=11

Part 2) y=7

Part 3) x=2

Part 4) y=2x-4

Part 5) 2x+3y=-10

Part 6) 2x-3y=-1

Step-by-step explanation:

Part 1) Write the standard form of the line that passes through the given points

(3, 1) and (-2, 3)

we know that

The equation of the line in standard form is equal to

Ax+By=C

where

A is a positive integer

B and C are integers

step 1

Find the slope m

m=(3-1)/(-2-3)

m=-2/5

step 2

Find the equation in point slope form

y-y1=m(x-x1)

we have

m=-2/5 and point (3,1)

substitute

y-1=-(2/5)(x-3)

y=-(2/5)x+(6/5)+1

y=-(2/5)x+(11/5)

Convert to standard form

Multiply by 5 both sides

5y=-2x+11

2x+5y=11 -----> equation in standard form

Part 2) Write the standard form of the line that passes through the given points

(4, 7) and (0, 7)

we know that

The equation of the line in standard form is equal to

Ax+By=C

where

A is a positive integer

B and C are integers

step 1

Find the slope m

m=(7-7)/(0-4)=0

This is a horizontal line (parallel to the x-axis)

The equation of the line is

y=7

Part 3) Write the standard form of the line that passes through the given points

(2, 3) and (2, 5)

we know that

The equation of the line in standard form is equal to

Ax+By=C

where

A is a positive integer

B and C are integers

step 1

Find the slope m

m=(5-3)/(2-2)

m=2/0 ----> the slope is undefined

This is a vertical line (parallel to the y-axis)

The equation of the line is

x=2

Part 4) Write the slope-intercept form of the line with a slope of 2 and a y -intercept of -4.

we know that

The equation of the line into slope-intercept form is equal to

y=mx+b

where

m is the slope and b is the y-intercept

we have

m=2

b=-4

substitute

y=2x-4

Part 5) Write the standard form of the line that is parallel to 2 x + 3 y = 4 and passes through the point (1, -4).

we know that

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

we have

2x+3y=4

isolate the variable y

3y=4-2x

y=(4/3)-(2/3)x

The slope of the given line is

m=-2/3

so

Find the equation of the line with slope m=-2/3 and passes through the point (1,-4)

y-y1=m(x-x1)

substitute

y+4=-(2/3)(x-1)

y=-(2/3)x+(2/3)-4

y=-(2/3)x-(10/3)

Convert to standard form

Multiply by 3 both sides

3y=-2x-10

2x+3y=-10

Part 6) Write the standard form of the line that contains a slope of 2/3 and passes through the point (1, 1)

Find the equation in point slope form

y-y1=m(x-x1)

we have

m=2/3 and point (1,1)

substitute

y-1=(2/3)(x-1)

y=(2/3)x-(2/3)+1

y=(2/3)x+(1/3)

Multiply by 3 both sides

3y=2x+1

2x-3y=-1

Mathematics

Which set represents the range of the function shown? (5 points) {(−1, 5), (2, 8), (5, 3), (13, −4)} a {−1, 2, 5, 13} b {−4, 3, 5, 8} c {(5, −1), (8, 2), (3, 5), (−4, 13)} d {−4, −1, 2, 3, 5, 5, 8, 13} Question 2 (5 points) (03.01 LC) Given that h(x) = 3x − 19, find the value of x that makes h(x) = 71. (5 points) a 30 b 43 c 52 d 194 Question 3 (5 points) (03.02 MC) Given the function g(x) = −3x + 4, compare and contrast g(−2) and g(4). Choose the statement that is true concerning these two values. (5 points) a The value of g(−2) is smaller than

Step-by-step answer

P Answered by PhD

1

1) b. {−4, 3, 5, 8}
2) a. 30
3) d. The value of g(−2) is larger than the value of g(4).
4) b. − 1 over 2
5) d. y = −2x − 1
6) a. line through the points 0 comma 6 and 12 comma 0
7) a. It is increasing during the time interval 4 < x < 7 hours.
8) from x15 to x 25 is 4 - -16 = -20 degree change
25-15 = 10000 feet
-20/10=-2 degrees every 1000 feet.
9) Suppose that the function f(x) is the parrent function and the graph of the function g(x)=f(x)-a can be obtained from the graph of the parrent function f(x) by shifting down a units.
Rewrite the expression for the function in the following way:
g(x)=32x-9=32x+8-8-9=32x+8-17=f(x)-17.
This shows that the shift down is made by 17 units.
10) b. The graph of y = f(x) will shift down 9 units.
11) b. y + 1 = 5(x + 2)
12) c. f(x) = 2x + 5
13) b. y = 9
14) d. vertical line through the point 5 comma 0

Mathematics

1. write the standard form of the line that passes through the given points. include your work in your final answer. (3, 1) and (-2, 3) 2. (4, 7) and (0, 7) 3. (2, 3) and (2, 5) 4.write the slope-intercept form of the line with a slope of 2 and a y -intercept of -4. include your work in your final answer. 5. write the standard form of the line that is parallel to 2 x + 3 y = 4 and passes through the point (1, -4). include your work in your final answer. 6. write the standard form of the line that contains a slope of 2/3 and passes through the point

Step-by-step answer

P Answered by PhD

8

Part 1) 2x+5y=11

Part 2) y=7

Part 3) x=2

Part 4) y=2x-4

Part 5) 2x+3y=-10

Part 6) 2x-3y=-1

Step-by-step explanation:

Part 1) Write the standard form of the line that passes through the given points

(3, 1) and (-2, 3)

we know that

The equation of the line in standard form is equal to

Ax+By=C

where

A is a positive integer

B and C are integers

step 1

Find the slope m

m=(3-1)/(-2-3)

m=-2/5

step 2

Find the equation in point slope form

y-y1=m(x-x1)

we have

m=-2/5 and point (3,1)

substitute

y-1=-(2/5)(x-3)

y=-(2/5)x+(6/5)+1

y=-(2/5)x+(11/5)

Convert to standard form

Multiply by 5 both sides

5y=-2x+11

2x+5y=11 -----> equation in standard form

Part 2) Write the standard form of the line that passes through the given points

(4, 7) and (0, 7)

we know that

The equation of the line in standard form is equal to

Ax+By=C

where

A is a positive integer

B and C are integers

step 1

Find the slope m

m=(7-7)/(0-4)=0

This is a horizontal line (parallel to the x-axis)

The equation of the line is

y=7

Part 3) Write the standard form of the line that passes through the given points

(2, 3) and (2, 5)

we know that

The equation of the line in standard form is equal to

Ax+By=C

where

A is a positive integer

B and C are integers

step 1

Find the slope m

m=(5-3)/(2-2)

m=2/0 ----> the slope is undefined

This is a vertical line (parallel to the y-axis)

The equation of the line is

x=2

Part 4) Write the slope-intercept form of the line with a slope of 2 and a y -intercept of -4.

we know that

The equation of the line into slope-intercept form is equal to

y=mx+b

where

m is the slope and b is the y-intercept

we have

m=2

b=-4

substitute

y=2x-4

Part 5) Write the standard form of the line that is parallel to 2 x + 3 y = 4 and passes through the point (1, -4).

we know that

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

we have

2x+3y=4

isolate the variable y

3y=4-2x

y=(4/3)-(2/3)x

The slope of the given line is

m=-2/3

so

Find the equation of the line with slope m=-2/3 and passes through the point (1,-4)

y-y1=m(x-x1)

substitute

y+4=-(2/3)(x-1)

y=-(2/3)x+(2/3)-4

y=-(2/3)x-(10/3)

Convert to standard form

Multiply by 3 both sides

3y=-2x-10

2x+3y=-10

Part 6) Write the standard form of the line that contains a slope of 2/3 and passes through the point (1, 1)

Find the equation in point slope form

y-y1=m(x-x1)

we have

m=2/3 and point (1,1)

substitute

y-1=(2/3)(x-1)

y=(2/3)x-(2/3)+1

y=(2/3)x+(1/3)

Multiply by 3 both sides

3y=2x+1

2x-3y=-1

Mathematics

Write the equation a. a line with slope 2/3 that passes through the point (-3,6) b. a line that passes through the points (3,-1)and (5,7)

Step-by-step answer

P Answered by PhD

1

$a)\ the\ slope-intercept\ form:\ y=mx+b\\--------------------------\\m=\frac{2}{3}\Rightarrow y=\frac{2}{3}x+b\\\\the\ point\ (-3;\ 6)\Rightarrow \frac{2}{3}\times(-3)+b=6\\\\-2+b=6\ \ \ \ \ |add\ 2\ to\ both\ sides\\\\b=8\\\\\boxed{y=\frac{2}{3}x+8}$

$b)\ the\ two-points\ formula:y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\-----------------------------\\the\ points:\ (3;-1);\ (5;\ 7)\\\\y-(-1)=\frac{7-(-1)}{5-3}(x-3)\\\\y+1=\frac{7+1}{2}(x-3)\\\\y+1=\frac{8}{2}(x-3)\\\\y+1=4(x-3)\\\\y+1=4x-12\ \ \ \ \ |subtract\ 1\ from\ both\ sides\\\\\boxed{y=4x-13}$

Write the equation a. a line with slope 2/3 that passes through the point (-3,6)b. a line that passe

Write the equation a. a line with slope 2/3 that passes through the point (-3,6)b. a line that passe

Mathematics

Find the value of r so the line that passes through each pair of points has the given slope. 40. in 1991, the federal minimum wage rate was $4.25 per hour. in 1997, it was increased to $5.15. find the annual rate of change in the federal minimum wage rate from 1991 to 1997. 41. (6,2), (9,r), m=-1 42. (4,-5), (3,r), m=8 43. (5,r), (2,-3), m=4/3 44. (-2,7), (r,3), m=4/3 45. (1/2, -1/4), (r,-5/4), m=4 46. (2/3, r), (1,1/2), m= 1/2 47. (4,r), (r,2), m=-5/3 48. (r, 5), (-2, r), m=-2/9

Step-by-step answer

P Answered by PhD

2

Slope is rise over run.
40. the rise is $0.90 and the run is 6 years, so the annual rate of change is .9/6 = $0.15 per year
40) Final $0.15 per year

For 41-48, find the difference between the given values of the same variable, then multiply by the slope and add/subtract from the variable whose second value is missing (sorry if that's confusing)
41. 9-6=3 => 3*(-1)=-3 => 2+3=-1
41) Final r=-1
42. 4-3=1 => 1*8=8 => (-5)-8=-13
42) Final r=-13
43. 5-2=3 => 3*(4/3)=4 => -3+4=1
43) Final r=1
44. 7-3=4 => 4*(3/4)=3 (flip the slop to find x values) => -2-3=-5
44) Final r=-5
45. (-1/4)-(-5/4)=4/4=1 => 1*(1/4)=1/4 (again flip the slope) => 1/2-1/4=1/4
45) Final r=1/4
46. 1-(2/3)=1/3 => (1/3)*(1/2)=(1/6) (don't have to flip this time) => (1/2)-(1/6)=1/3
46) Final r=1/3
For 47 and 48, I'll setup an equation for r
47. (4-r)*(-5/3)=r-2 => -20/3+(5r)/3=r-2 => -14/3+(5r)/3=r => -14/3=-(2r)/3 => -14=-2r => r=7
47) Final r=7
48. (R-(-2))*(-2/9)=5-r => -2(r+2)/9=5-r => -(2r)/9-4/9=5-r => -(2r)/9=49/9-r => (7r)/9=49/9 => 7r=49 => r=7
48) Final r=7

Hope I helped :)

What is the equation of the line that passes through the point (3,7) and has a slope of 2/3

Step-by-step answer

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