The answer is y=3/2 x +5
Slope intercept form means we're looking for an equation that looks like y = mx +b. We need to use the given two points to find the slope, m, and the y-intercept, b.
To find m, we need to find the change in y between two points over the change in x (or "rise over run"). To do this, we use the equation: m = (y_2 - y_1)/(x_2 - x_1) .
Using the points (-2,2) and (0,5) as (x_1,y_1) and (x_2,y_2), we get m = (5 - 2)/(0 - -2) = 3 / 2
To find b, we look back at the equation y = mx +b. We now know m and can use the x and y from either of our points. I'll use (-2, 2), but as you'll see in a moment, we already know b from our other point.
Using m = 3/2, x=-2, and y=2:
y = mx +b becomes 2 = 3/2 * -2 + b.
Now we solve for b:
2 = 3/2 * -2 + b
Simplify:
2 = -3 + b
Add 3 to both sides:
5 = b
We now know both m and b, so our slope-intercept equation becomes:
y=3/2 x +5
That 5 sure looks familiar... the point (0,5) actually gives us b for free since the y-intercept is the point where the line crosses the y-axis, which is true when x=0. This short cut can help you save time, but you should also make sure you know how to find b when you don't get so lucky!