Answer:
[tex] y = x - 2 [/tex]
Step-by-step explanation:
The slope-intersect form of the equation of a line is:
[tex] y = mx + b [/tex]
where m is the slope, and (0, b) is the y-intercept.
First, look at the y-intercept. The y-intercept is the point of intersection of the line and the y-axis. In this case, the point of intersection is (0, -2). That means that b = -2.
Now we find the slope. We see two points on the line, (0, -2) and (3, 1). Start at (0, -2). To go from point (0, -2) to point (3, 1), first you go 3 units up. That is a change in y of +3. Then you go 3 units right. That is a change in x of +3.
[tex] slope = m = \dfrac{change in y}{change in x} [/tex]
Now we can find the slope of this line.
[tex] slope = m = \dfrac{change in y}{change in x} = \dfrac{3}{3} = 1 [/tex]
Now that we know the slope, 1, and the y-intercept, -2, we use the first equation above to write the equation of the line in the slope-intercept form.
[tex] y = mx + b [/tex]
[tex] y = 1x + (-2) [/tex]
[tex] y = x - 2 [/tex]
