We know that f(x) is a linear function.
We also know two points of the function:
[tex]\begin{gathered} f(-2)=-3 \\ f(1)=4 \end{gathered}[/tex]We can calculate the slope of f(x) as:
[tex]\begin{gathered} m=\frac{f(x_2)-f(x_1)}{x_2-x_1} \\ m=\frac{4-(-3)}{1-(-2)} \\ m=\frac{4+3}{1+2} \\ m=\frac{7}{2} \\ m=3.5 \end{gathered}[/tex]With the slope m = 3.5 and one point, like (1, 4), we can write the equation in slope-point form and then rearrange:
[tex]\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}[/tex]Answer: the equation is f(x) = 3.5x + 0.5
