Chapter 5, Problem 5CR

To determine

To graph: The line $2x-4y=16$ .

Explanation of Solution

Given information:

The equation of line $2x-4y=16$ .

Graph:

To graph a linear equation, at least two $\left(x,y\right)$ points are required. It can be graphed by finding $x$ and $y$ intercepts also.

To find $x-$ intercept of the line $2x-4y=16$ , substitute $y=0$ and solve for $x$ .

  $\Rightarrow 2x-4\left(0\right)=16$

  $\Rightarrow 2x-0=16$

  $\Rightarrow 2x=16$

Divide both sides by $2$ ,

  $\Rightarrow \frac{2x}{2}=\frac{16}{2}$

  $\Rightarrow x=8$

Therefore, $x-$ intercept of the line $2x-4y=16$ is $\left(8,0\right)$ .

To find $y-$ intercept of the line $2x-4y=16$ , substitute $x=0$ and solve for $y$ .

  $\Rightarrow 2\left(0\right)-4y=16$

  $\Rightarrow 0-4y=16$

  $\Rightarrow -4y=16$

Divide both sides by $-4$ ,

  $\Rightarrow \frac{-4y}{-4}=\frac{16}{-4}$

  $\Rightarrow y=-4$

Therefore, $y-$ intercept of the line $2x-4y=16$ is $\left(0,-4\right)$ .

Plot both points $\left(8,0\right),\left(0,-4\right)$ on $xy-$ plane, and join them by a straight line.

Therefore, graph of line $2x-4y=16$ is:

  

Interpretation:

The graph represents the linear equation $2x-4y=16$ with $x-$ intercept $\left(8,0\right)$ and $y-$ intercept $\left(0,-4\right)$ .