Q. 13 - Precalculus Enhanced with Graphing Utilities

Question

Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.

$y=2x+8$.

Step-by-Step Solution

Answer

The intercepts are :

x-intercept is $\left(-4, 0\right)$and y-intercept is $\left(0, 8\right)$

Step 1: Given information:

Consider the equation,

$y=2x+8$.

Step 2: To find the x-intercept:

Let $y=0$ in the equation,

Then $0=2x+8$

    $0-8=2x+8-8$  [ add (-8)  on both sides. ]

      $-8=2x$

     $\frac{2x}{2}=\frac{-8}{2}$  [ Divide by 2 on both sides. ]

         $x=-4$

$x-intercept is \left(-4, 0\right).$

Step 3: To find the y-intercept:

Let $x=0$ in the equation,

Then $y=2\times 0+8$

          $y=8$

$y-intercept is \left(0, 8\right).$

Step 4: To draw the graph:

We can draw the graph of the equation $y=2x+8$ by plotting the above intercepts and the points in the table below,

x	$y=2x+8$	$\left(x,y\right)$
-6	-4	$\left(-6,-4\right)$
-2	4	$\left(-2,4\right)$
2	12	$\left(2,12\right)$