Question

2. What is the slope-intercept equation for the graph shown below? 5+ 4 3 2 11 -6 -5 -4 -3 -2 -1 2 3 4 5 -2. -3 -5 -6 A. y = x + 2 B. y = 2x + 2 C. y=1/2x-1. D. y=2x-1

Answer 1

Recall that the slope-intercept equation of a line is given by the formula y=mx+b where m is the slope and b is the y intercept.

To find the value of b, we simply see the value of the function at x=0. From the graph, we see that whenever x=0 the value of y is -1. This leads to b=-1.

Now, to calculate the slope, we take two points from the line. Let us take the points (0,-1) and (2,0). We proceed as follows:

Recall that given points (a,b) and (c,d) the slope of the line that passes through them is given by the formula

$m=\frac{d-b}{c-a}=\frac{b-d}{a-c}$

In our case, we take a=0,b=-1, c=2 and d=0, so we get

$m=\frac{-1-0}{0-2}=\frac{-1}{-2}=\frac{1}{2}$

so we get that the line equation of the graph in slope intercept form is

$y=\frac{1}{2}x-1$