SOLUTION: f is a linear function. If f(5) = -5 and f(-25) = -25, find f(2) and f(50). Thank you so much for helping me!

Question 267648: f is a linear function.
If f(5) = -5 and f(-25) = -25, find f(2) and f(50).

Thank you so much for helping me!
Answer by roseo(33) (Show Source): You can put this solution on YOUR website!
Think of f(5)=-5 and f(-25) = -25 as points (5,-5) and (-25,-25). Use these 2 points to write the equation of the line that passes through them (because the problem said that this was a linear function). First find the slope
(-25--5)/(-25-5) = -20/30 which is -2/3. Using the slope intercept form of the line we would have y=-2/3x + b the plug in one of the points to find b. I will use (5,-5)
-5=-2/3(5)+b
-5 = -10/3+b
-5+10/3 = b
-15/3 +10/3 = b
-5/3 = b
Our function is y=-2/3x-5/3
so f(2) = -2/3(2)-5/3
-4/3-5/3
=-9/3
=-3
f(50) = -2/3(50)-5/3
=-100/3-5/3
=-105/3
=-35
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