Question

How do you find the important points to graph `f (x) = -3x + 8`?

Answer 1

The first thing to note is that this is a polynomial of degree 1. Hence this is a straight line. The points that are of important for sketching any straight line are the intercepts.

To find the x-intercept (where the curve "cuts" the x-axis), we solve for `f(x)=0`
That is, `-3x+8=0`
Then, `8=3x`
`:. x=8/3`

To find the y-intercept (where the graph cuts the y-axis), we let `x=0` and solve.
That is, `f(x)=y=-3(0)+8`
`:. y=8`

So we have the points `(0,8)` and `(8/3,0)`. To draw the graph, simply plot the points and draw a line passing through them. graph{-3x+8 [-10, 10, -5, 5]}