Question

Use the graph to find the intercepts. Remember to write the slope as a "reduced fraction. Then, write the equation of the line in slope-intercept form.

Answer 1

First, take a look at the vertical axis. Its. equation is x=0. count the number of scale divisions from the origin to the point where the line crosses the vertical axis. It's 4. Thus, the vertical intercept is (0,4).

Next, determine the x value where the line crosses the horizontal axis. It's 4, and so the horiz. intercept is (4,0).

Going from (0,4) to (4,0), x increases by 4 and y decreases by 4. Thus, the slope of the given line is m = rise / run = -4/4 = -1.

Starting with y = mx + b, substitute the knowns:

b, the y-intercept, is 4. m, the slope, is -1. Thus, the equation of this line in slope-intercept form is y = -x + 4.

Answer 2

Look at the pictures.

The slope-intercept form:

`y=mx+b`

m - slope
`\to m=(y_2-y_1)/(x_2-x_1)`

b - y-intercept

(1)

x-intercept = 4

y-intercept = 4 → b = 4

We have the points (0, 4) and (4, 0). Substitute:

`m=(0-4)/(4-0)=(-4)/(4)=-1`

Slope = -1

Equation: y = -x + 4

(2)

x-intercept = 6

y-intercept = -4 → b = -4

We have the points (0, 6) and (-6, 0). Substitute:

`m=(0-6)/(-6-0)=(-6)/(-6)=1`

Slope = 1

Equation: y = x - 4

(3)

x-intercept = 5

y-intercept = -3 → b = -3

We have the points (5, 0) and (0, -3). Substitute:

`m=(-3-0)/(0-5)=(-3)/(-5)=(3)/(5)`

Slope =
`(3)/(5)`

Equation:
`y=(3)/(5)x-3`