Question

If y = f(x) is a linear function such that f(5) = 24 and f (17) = 120, then f(x) =

Answer 1

We know that f(x) is a linear function so first we need to calculate first the slope

$m=\frac{y_2-y_1}{x_2-x_1}$

where in our case

y1=24, x1=5

y2=120, x2=17

we substitute the values

$m=\frac{120-24}{17-5}=\frac{96}{12}=8$

then we will use the form of slope-point in order to find the y-interceot}

$y-24=8(x-5)$

then we isolate the y

$\begin{gathered} y-24=8x-40 \\ y=8x-40+24 \\ y=8x-16 \end{gathered}$

therefore for f(x)

$f(x)=8x-16$