Another one like that last one, huh? Okay, so the equation is y = mx + b.
y would be your final answer, and we don't have that yet. m is the average rate of change. and b is your y-intercept. we're going to have to find both your average rate of change and your y-intercept, since your y-intercept isn't listed above.
so your m is your average rate of change. we'd take two points, and use that formula : [tex] \frac{y(2) - y(1)}{x(2) - x(1)} [/tex].
We'll use the points (2,-1) and (4, -5). When we substitute the formula, we would get [tex] \frac{-5-(-1)}{4-2} [/tex].
So we do the negatives and everything, and it ends up as [tex] \frac{-4}{2} [/tex]. Once you divide that, you end up with -2. So your m is -2. Your average rate of change is -2. We can fill in one blank in that equation now.
y = -2x + b
Then there's the matter of finding your y-intercept. To find your y-intercept, you would have to take any point from the chart. Note that finding your y-intercept isn't really related to your average rate of change.
So you take any point. Say you take (2,-1). To find your y-intercept, you would substitute the y = mx + b thing here again. Your y-intercept in the point you chose will be the y, your average rate of change which we already found is your average rate of change, and your x-value will be the x-intercept of the point we're using. That would make it :
-1 = -2(2) + b (you would leave the b as is here.)
-1 = -4 + b
Add four to both sides, you end up with 3 = b.
Your final answer is y = -2x + 3. (God, this was pretty long.)
