First you need to find the slope of the line containing those 2 points using the slope formula. Filling in with our info we have $m= \frac{-6-3}{4-(-2)}=- \frac{9}{6}=- \frac{3}{2}$ . So the slope is -1.5. Now we need to find out the rest of the info, mainly the y-intercept. The line appears to go through the y axis at (0, 0), but let's make sure. We will use the slope we just found and one of our points to solve for the y-intercept. I picked point (4, -6). Filling in to solve for b we get -6 = (-1.5)(4) + b. Doing the multiplication on the right gives us -6=-6 + b. Add 6 to both sides to get that b = 0. Now let's use that and the slope we found to rewrite the equation in slope-intercept form. y = -1.5x + 0 or y = -1.5x and there you go!

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3 years ago