Question

The graph shows a linear relationship between x and y. What is the rate of change of y with respect to x for this function?

A) 2
B) -2
C) -1/2
D) 1/2

Answer 1

A) 2

Explanation:

Rise over run,

`(y_(2) -y_(1) )/(x_(2) -x_(1))`

-2 will be
`x_(1)` and -3 will be
`y_(1)`

2 will be
`x_(2)` and 5 will be
`y_(2)`

It doesn't matter which order you place the points, for
`x_(1)`, or
`x_(2)` but
`x_(1)` and and
`y_(1)` must be one point while
`x_(2)` and
`y_(2)` must be one point.

Then, we replace the values to find:

`(5-(-3))/(2-(-2))`

We then simplify this expression to
`(8)/(4) = 2`

Therefore, our slope for this function is 2

Answer 2

A

Explanation:

the slope of the line is a measure of the rate of change.

calculate the slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 2, - 3) and (x₂, y₂ ) = (2, 5) ← 2 points on the line

m =
`(5-(-3))/(2-(-2))` =
`(5+3)/(2+2)` =
`(8)/(4)` = 2

the rate of change of y with respect to x is 2