Chapter 13, Problem 20CR

To determine

To graph: $x+2y=4$

Explanation of Solution

Given$x+2y=4\Rightarrow y=\frac{4-x}{2}$

  

Interpretation: Let $f(x)=-x$ .

i.e. $f(x)=-x$ passes through origin and passing through $(1,-1)$

If the graph of $y=f\left(x\right)$ is shifted vertically upward by $c$ unit, where $c>0$ then the equation of the transformed graph will be $g(x)=f(x)+c$

Here $g(x)=4-x\Rightarrow 4+f(x)$

Therefore the graph $f(x)$ shifts vertically by 4 units upward

Now, $g(x)=4-x$

If the graph $y=g(x)$ shrink vertically by $c$ units, $c>0$ , then the equation of transformed graph will be $h(x)=\frac{g(x)}{c}$

Here $h(x)=\frac{4-x}{2}\Rightarrow c=2$ , therefore the graph shrinks vertically by 2 units.