Mathematics, 07.12.2020 05:10 smilebehappy468

The graph of a linear function is shown on the grid. What is the rate of change of y with respect to x for this function? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.

The graph of a linear function is shown on the grid. What is the rate of change of y with respect t

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Answer from: sunflowergirl6664

This question is based on the concept of equation of line. Therefore, the y = -0.2 x + 3 is the rate of change of y with respect to x for this function.

We need to determined the the rate of change of y with respect to x for this function.

According to the question,

A linear relationship of line can be written as:

y = a $\bold{\times}$ x + b

Where, a is the slope ( rate of change of y with respect to x) and b is the y-axis intercept.

For a line that passes through the points $\bold{(x_1, y_1) }$ and $\bold{(x_2, y_2)}$ . Thus, the slope can be written as:

$a = \dfrac{(y_2- y_1) }{(x_2 - x_1)}$

It is given that, the points are (-3, 3.6) and (5, 2) . Then the slope will be:

$\bold{a = \dfrac{(2- 3.6) }{( 5- (-3) )} = \dfrac{-1.6}{8} = -0.2}$

Then the rate of change is -0.2.

Now, the equation of line become,

y = -0.2 x + b

Now, find the value of b, we can simply replace the values of one of the points in that equation, use the point (5, 2) .This means that we must replace x by 5, and y by 2.

2 = -0.2*5 + b

2 = -1 + b

2 + 1 = b

3 = b

Then the equation is: y = -0.2 x + 3.

Therefore, the y = -0.2 x + 3 is the rate of change of y with respect to x for this function.

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Answer from: sofia467735

A linear relationship can be written as:

y = a*x + b

where a is the slope (also called the rate of change of y with respect to x) and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case, we have the points (-3, 3.6) and (5, 2)

Then the slope will be:

a = (2 - 3.6)/(5 - (-3)) = (-1.6/8) = -0.2

Then the rate of change is -0,2

We could complete the equation for the line.

At the moment we know that:

y = -0.2*x + b

To find the value of b, we can simply replace the values of one of the points in that equation, i will use the point (5, 2)

This means that we must replace x by 5, and y by 2

2 = -0.2*5 + b

2 = -1 + b

2 + 1 = b

3 = b

Then the equation is:

y = -0.2*x + 3.

Answer from: Quest

Idon’t know what the answer is i wish i could

Answer from: Quest

3/8

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The graph of a linear function is shown on the grid. What is the rate of change of y with respect to...