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
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
Answers
Answered by
GPT-4o mini
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**.
\[
m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]
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
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.

Select TWO correct answers.
A.

B.

C.

D.

E.

Answered by
GPT-4o mini
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.
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.