Mathematics: Describe how the graph of y=2x is different from the graph of y=2x - 7. Explain or show your reasoning.

Describe how the graph of y=2x is different from, №9246525, 28.07.2021 13:01

Mathematics

Describe how the graph of y = 2x is the same and different from the graph of y = 2x - 7 explain or show your reasoning

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They are the same because they have the same slope but are different because they have different y intercepts.

Step-by-step explanation:

Mathematics

Describe how the graph of y = 2x is the same and different from the graph of y = 2x - 7 explain or show your reasoning

Step-by-step answer

P Answered by PhD

21

They are the same because they have the same slope but are different because they have different y intercepts.

Step-by-step explanation:

Mathematics

Test due 12/1 the function f(x) = x − 1 is changed to f(x) = 1 4 x − 1. which describes the effect of the change on the graph of the original function? a) the line will be steeper. b) the line will be less steep. c) line changes from increasing to decreasing. d) line changes from decreasing to increasing. 2) sketch the linear function f(x) = 1 6 (3x + 1). which key feature of the graph is true? a) y-intercept (0, 1) b) x-intercept ( 1 6 , 0) c) x-intercept (− 1 3 , 0) d) y-intercept (0, − 1 6 ) 3) the graph of the line y = 4 is a a) vertical line

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1

1. f(x) = 1/4x − 1. B)The line will be less steep. The slope is lower now

2. C)x-intercept (−1/3 , 0). Replacing f(x) = 0 we get x = -1/3

3. B)horizontal line with a slope of zero. The slope is 0 because there is no x in the equation.

4. D)Line changes from decreasing to increasing. The slope changed from negative to positive.

5. See first graph attached

6. See second graph attached. g(x) = (1/3)*x

7. C)The rate of change is different, but the y-intercepts are the same. The rate of change of Mike is negative because he withdraws $25 each week. The y-intercepts of Mike is $200 because that was his initial deposit.

8. B)shifts the line 7 units down. f(x-7) translates f(x) 7 units to the right, given the slope is positive ( = 1) then f(x) is translated 7 units down.

9. No graph is shown

10. C)g(x) = x - 3. g(x) = f(x) - 3, so g(x) is f(x) translated 3 units down.

Test due 12/1 the function f(x) = x − 1 is changed to f(x) = 1 4 x − 1. which describes the effect o

Mathematics

Test due 12/1 the function f(x) = x − 1 is changed to f(x) = 1 4 x − 1. which describes the effect of the change on the graph of the original function? a) the line will be steeper. b) the line will be less steep. c) line changes from increasing to decreasing. d) line changes from decreasing to increasing. 2) sketch the linear function f(x) = 1 6 (3x + 1). which key feature of the graph is true? a) y-intercept (0, 1) b) x-intercept ( 1 6 , 0) c) x-intercept (− 1 3 , 0) d) y-intercept (0, − 1 6 ) 3) the graph of the line y = 4 is a a) vertical line

Step-by-step answer

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1

1. f(x) = 1/4x − 1. B)The line will be less steep. The slope is lower now

2. C)x-intercept (−1/3 , 0). Replacing f(x) = 0 we get x = -1/3

3. B)horizontal line with a slope of zero. The slope is 0 because there is no x in the equation.

4. D)Line changes from decreasing to increasing. The slope changed from negative to positive.

5. See first graph attached

6. See second graph attached. g(x) = (1/3)*x

7. C)The rate of change is different, but the y-intercepts are the same. The rate of change of Mike is negative because he withdraws $25 each week. The y-intercepts of Mike is $200 because that was his initial deposit.

8. B)shifts the line 7 units down. f(x-7) translates f(x) 7 units to the right, given the slope is positive ( = 1) then f(x) is translated 7 units down.

9. No graph is shown

10. C)g(x) = x - 3. g(x) = f(x) - 3, so g(x) is f(x) translated 3 units down.

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

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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

1. which data set represents an increasing, linear function? (1 point) a. (1,-,,,7) b. (1,1) (2,0), (3,-1), (4,-2) c.(1,-,,11) (7, 18) d.(1, 17), (2,15), (3,11), (4, 3) 2.which function s graph passes through the points (1, 4), (2, 9) and (3, 16) a. y = 5x + 4 b. y = (x + 1) mini 2 on the end c. y = (x + 3) mini 2 on the end d. y = 7x - 5 3. suppose that after one warm-up lap around a track, you run 10 laps an hour. what is an equation that represents the total numver of laps you ve run, y in terms of the number of the hours you run, t? a. y(t)

Step-by-step answer

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63

#1) A
#2) B
#3) C
#5) A
#7) D
#10) D
#11) D
#14) A
#15) D
#16) A
#19) D

Explanation
#1) If the data set is linear, the slope will be constant throughout the entire data set. For data set A, the slope between the first two points is:
m = (y₂-y₁)/(x₂-x₁) = (1--2)/(3-1) = 3/2
Between the second two points,
m=(4-1)/(5-3) = 3/2
Between the third pairs of points,
m=(7-4)/(7-5) = 3/2

The slope is constant throughout the entire set. The set is also increasing; as x increases, y increases as well.

#2) Substituting 4 for y and 1 for x,
y = (x+1)²
4 = (1+1)² = 2²
9 = (1+2)² = 3²
16 = (1+3)² = 4²
This works for each point, so this is the solution.

#3) Since he runs 10 laps per hour t, this is 10t. Adding the first lap to this, we get y=10t+1.

#5) If a sequence is arithmetic, each term is found by adding a constant (called the common difference) to the previous term. If the common difference is 2, this means that 2 was added each time. This only works for choice A.

#7) For x to vary directly as y, this means that y/x = k; in other words, the quotient of y and x is constant for every point.

#10) The formula for slope is:
m=(y₂-y₁)/(x₂-x₁)

Using the information we're given, we have
3=(d-5)/(4-2)
3=(d-5)/2

Multiply both sides by 2:
3*2 = ((d-5)/2)*2
6 = d-5

Add 5 to both sides:
6+5 = d-5+5
11 = d

#11) Using point slope form,
y-y₁ = m(x-x₁)
y-1 = 3(x--2)
y-1 = 3(x+2)

Using the distributive property,
y-1 = 3*x + 3*2
y-1 = 3x + 6

Add 1 to both sides:
y-1+1 = 3x+6+1
y=3x+7

#14) If two lines are parallel, they have the same slope. The slope of the given equation is 4; the only one with a slope of 4 is A.

#15) If two lines are perpendicular, they have slopes that are negative reciprocals (opposite signs and flipped). The slope of the given equation is 2; this means the slope of the perpendicular line would be -1/2. The only one with this slope is D.

#16) The two equations are not the same, so there are not infinitely many solutions. The variables do not both cancel, so there is at least one solution. This only leaves one solution as the answer.

#19) Using 1 for 7 and 4 for x, we check each equation. The only one that comes out correct is D.

Mathematics

1. which data set represents an increasing, linear function? (1 point) a. (1,-,,,7) b. (1,1) (2,0), (3,-1), (4,-2) c.(1,-,,11) (7, 18) d.(1, 17), (2,15), (3,11), (4, 3) 2.which function s graph passes through the points (1, 4), (2, 9) and (3, 16) a. y = 5x + 4 b. y = (x + 1) mini 2 on the end c. y = (x + 3) mini 2 on the end d. y = 7x - 5 3. suppose that after one warm-up lap around a track, you run 10 laps an hour. what is an equation that represents the total numver of laps you ve run, y in terms of the number of the hours you run, t? a. y(t)

Step-by-step answer

P Answered by PhD

63

#1) A
#2) B
#3) C
#5) A
#7) D
#10) D
#11) D
#14) A
#15) D
#16) A
#19) D

Explanation
#1) If the data set is linear, the slope will be constant throughout the entire data set. For data set A, the slope between the first two points is:
m = (y₂-y₁)/(x₂-x₁) = (1--2)/(3-1) = 3/2
Between the second two points,
m=(4-1)/(5-3) = 3/2
Between the third pairs of points,
m=(7-4)/(7-5) = 3/2

The slope is constant throughout the entire set. The set is also increasing; as x increases, y increases as well.

#2) Substituting 4 for y and 1 for x,
y = (x+1)²
4 = (1+1)² = 2²
9 = (1+2)² = 3²
16 = (1+3)² = 4²
This works for each point, so this is the solution.

#3) Since he runs 10 laps per hour t, this is 10t. Adding the first lap to this, we get y=10t+1.

#5) If a sequence is arithmetic, each term is found by adding a constant (called the common difference) to the previous term. If the common difference is 2, this means that 2 was added each time. This only works for choice A.

#7) For x to vary directly as y, this means that y/x = k; in other words, the quotient of y and x is constant for every point.

#10) The formula for slope is:
m=(y₂-y₁)/(x₂-x₁)

Using the information we're given, we have
3=(d-5)/(4-2)
3=(d-5)/2

Multiply both sides by 2:
3*2 = ((d-5)/2)*2
6 = d-5

Add 5 to both sides:
6+5 = d-5+5
11 = d

#11) Using point slope form,
y-y₁ = m(x-x₁)
y-1 = 3(x--2)
y-1 = 3(x+2)

Using the distributive property,
y-1 = 3*x + 3*2
y-1 = 3x + 6

Add 1 to both sides:
y-1+1 = 3x+6+1
y=3x+7

#14) If two lines are parallel, they have the same slope. The slope of the given equation is 4; the only one with a slope of 4 is A.

#15) If two lines are perpendicular, they have slopes that are negative reciprocals (opposite signs and flipped). The slope of the given equation is 2; this means the slope of the perpendicular line would be -1/2. The only one with this slope is D.

#16) The two equations are not the same, so there are not infinitely many solutions. The variables do not both cancel, so there is at least one solution. This only leaves one solution as the answer.

#19) Using 1 for 7 and 4 for x, we check each equation. The only one that comes out correct is D.

Mathematics

Imran is paid ?286 per week Every week he puts 20% of his wage into a savings account How much does he put into his savings each week

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The answer is in the image