Problem: Linear functions and the delta-notation

Problem

A linear function has slope \(a=7/3\) .

  1. If \(x\) increases by one unit ( \(Δx=1\) ), find the increase in \(y\) (find \(Δy\) )
  2. If \(x\) increases by nine units ( \(Δx=9\) ), find the increase in \(y\) (find \(Δy\) )
  3. If \(x\) decreases by one unit ( \(Δx=-1\) ), find the increase in \(y\) (find \(Δy\) )
  4. If \(x\) decreases by nine units ( \(Δx=-9\) ), find the increase in \(y\) (find \(Δy\) )
  5. You know that the increase in \(y\) was \(9/2\) ( \(Δy=-9\) ). What was the increase in \(x\) ? (find \(Δx\) )

(A negative increase is the same as a decrease)

Solution