Question

What are the slope and the y-intercept of the linear function that is represented by the graph?

On a coordinate plane, a line goes through points (negative 3, 0) and (negative 2, 4).
The slope is 3, and the y-intercept is 9.
The slope is 3, and the y-intercept is 12.
The slope is 4, and the y-intercept is 9.
The slope is 4, and the y-intercept is 12.

Answer 1

***Calculate the slope:
m = (y2 - y1)/(x2 - x1)

Let (-3,0) be Point 1 and (-2,4) be Point 2. We can then assign:
y2 = 4
y1 = 0
x2 = -2
x1 = -3

Substitute:
m = (4 - 0)/(-2 - (-3)) => 4/(-2 + 3) => 4/1 => 4

The slope is 4.


***Find the y-intercept:
Use point-slope form, which is (y - y1) = m(x - x1) and manipulate it into slope-intercept form, which is y = mx + b. b is our y-intercept.

We had:
y1 = 0
x1 = -3
m = 4

Substitute and manipulate:
y - 0 = 4(x - (-3)) => y = 4(x + 3) => y = 4x + 12.

The y-intercept is 12.


***Final answer: The slope is 4, and the y-intercept is 12.

Answer 2

Slope m = (4 − 0)/(-2 − (-3)) = 4/1 = 4.
Using (-3,0): y = 4(x + 3) = 4x + 12, so y-intercept is 12.

Answer: slope 4, y-intercept 12.