Question

If f(x) is a linear function, f( – 2) = – 3, and f(1) = 4, find an equation for f(x)-f(x) =

Answer 1

We know that f(x) is a linear function.

We also know two points of the function:

`\begin{gathered} f(-2)=-3 \\ f(1)=4 \end{gathered}`

We can calculate the slope of f(x) as:

`\begin{gathered} m=(f(x_2)-f(x_1))/(x_2-x_1) \\ m=(4-(-3))/(1-(-2)) \\ m=(4+3)/(1+2) \\ m=(7)/(2) \\ m=3.5 \end{gathered}`

With the slope m = 3.5 and one point, like (1, 4), we can write the equation in slope-point form and then rearrange:

`\begin{gathered} y-y_0=m(x-x_0) \\ y-4=3.5(x-1) \\ y-4=3.5x-3.5 \\ y=3.5x-3.5+4 \\ y=3.5x+0.5 \end{gathered}`

Answer: the equation is f(x) = 3.5x + 0.5