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

Look at the pictures.

The slope-intercept form:

$y=mx+b$

m - slope $\to m=\dfrac{y_2-y_1}{x_2-x_1}$

b - y-intercept

(1)

x-intercept = 4

y-intercept = 4 → b = 4

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

$m=\dfrac{0-4}{4-0}=\dfrac{-4}{4}=-1$

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:

$m=\dfrac{0-6}{-6-0}=\dfrac{-6}{-6}=1$

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:

$m=\dfrac{-3-0}{0-5}=\dfrac{-3}{-5}=\dfrac{3}{5}$

Slope = $\dfrac{3}{5}$

Equation: $y=\dfrac{3}{5}x-3$

Answer 2

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.