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!