How do you write an equation in slope intercept form given that the line passes through the points (-2, 2) and (0,5)?

1 Answer
Jun 3, 2015

The answer is y=3/2 x +5y=32x+5

Slope intercept form means we're looking for an equation that looks like y = mx +by=mx+b. We need to use the given two points to find the slope, mm, and the y-intercept, bb.

To find mm, 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) m=y2y1x2x1.

Using the points (-2,2)(2,2) and (0,5)(0,5) as (x_1,y_1)(x1,y1) and (x_2,y_2)(x2,y2), we get m = (5 - 2)/(0 - -2) = 3 / 2 m=5202=32

To find bb, we look back at the equation y = mx +by=mx+b. We now know mm and can use the xx and yy from either of our points. I'll use (-2, 2)(2,2), but as you'll see in a moment, we already know bb from our other point.

Using m = 3/2m=32, x=-2x=2, and y=2y=2:
y = mx +by=mx+b becomes 2 = 3/2 * -2 + b2=322+b.

Now we solve for bb:
2 = 3/2 * -2 + b2=322+b

Simplify:
2 = -3 + b2=3+b

Add 33 to both sides:
5 = b5=b

We now know both mm and bb, so our slope-intercept equation becomes:
y=3/2 x +5y=32x+5

That 55 sure looks familiar... the point (0,5)(0,5) actually gives us bb for free since the y-intercept is the point where the line crosses the y-axis, which is true when x=0x=0. This short cut can help you save time, but you should also make sure you know how to find bb when you don't get so lucky!