linear function

Question

Find a linear function h, given h(6)=-13 and h(-2)=11. Then find h(9)

Answer 1

When the x value goes up by 8 (from -2 to +6), the value of the function goes down by 24 (from +11 to -13). This means the slope (change in y over change in x) of the line is 24/-8 = -3.

Now that you know the slope, you can start putting together a linear function in the form "y = mx + b" and you know that m is -3. Plug this in for one of the points you are given and you can figure out the value for b (the y-intercept).

For example, h(6) = -3(6) + b = -18 + b which equals -13. Add 18 to both sides of the equation and you see that the value of b must be +5. Check this with the other point: h(-2) = -3(-2) + 5 = +6 +5 = 11 yep that works!

So now you have to find h(9), just plug 9 into the equation h(x) = -3x +5 = -3(9) +5 = -27 +5 = -22

Hope that helps.