Question

The table below represents some points on the graph of a linear function.
 x 5 2 −1 −4 −7 −10
y −15 −10 −50 5 10
What is the rate of change of y with respect to x for this function?

A.

−3/5

B.

3/5

C.

5/3

D.

-5/3

Answer 1

Line l is drawn on a coordinate plane and has the equation 3y + 15 = x. Select all the tables of values that represent a line with a greater rate of change than Line l.

Select TWO correct answers.

A.



B.



C.



D.



E.



Answer 2

To find the rate of change of \(y\) with respect to \(x\), we need to determine the slope of the linear function. The slope \(m\) can be calculated using the formula:

\[
m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

We can select any two points from the provided data. Let's choose the first two points:

1. \( (5, -15) \)
2. \( (2, -10) \)

Now, we'll plug these values into the slope formula:

\[
m = \frac{-10 - (-15)}{2 - 5} = \frac{-10 + 15}{2 - 5} = \frac{5}{-3} = -\frac{5}{3}
\]

Thus, the rate of change of \(y\) with respect to \(x\) is \(-\frac{5}{3}\).

The answer is **D. -5/3**.

Answer 3

To determine which tables of values represent lines with a greater rate of change than Line \( l \) given by the equation \( 3y + 15 = x \), let's first find the slope (rate of change) of Line \( l \).

1. Rearranging the equation to slope-intercept form \( y = mx + b \):

\[
3y + 15 = x
\]

Subtract 15 from both sides:

\[
3y = x - 15
\]

Now divide each term by 3:

\[
y = \frac{1}{3}x - 5
\]

This shows that the slope (rate of change) of Line \( l \) is \( \frac{1}{3} \).

2. A line with a greater rate of change will have a slope greater than \( \frac{1}{3} \).

Now, you will need to check the tables of values provided in options A, B, C, D, and E to determine the slopes of these lines. The slope can be calculated from any two points in each table using the formula:

\[
m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

I cannot see the tables as they are not provided in the text. However, if you provide the data in those tables, I can help you calculate the slopes and determine which two have a greater rate of change than Line \( l \). Please share the content of options A, B, C, D, and E.