Q. 11 - Precalculus Enhanced with Graphing Utilities

Question

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

y = x + 2

Step-by-Step Solution

Answer

The intercepts are :

x-intercept is $(-2, 0)$ and y-intercept is $(0, 2)$.

Step 1: Given information:

Consider the equation, 

y = x + 2

Step 2: To find the x-intercept:

Let $y=0$ in the given equation,

Then, $0=x+2$

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

         $-2=x$

The solution is $x=-2$.

$x-intecept is (-2, 0).$

Step 3: To find the y-intercept:

Let $x=0$ in the given equation,

then $y=0+2$

        $y=2$

$y-intercept is (0, 2).$

Step 4: To draw the graph:

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

x	$y=x+2$	$\left(x,y\right)$
-1	1	$\left(-1,1\right)$
1	3	$\left(1,3\right)$
2	4	$\left(2,4\right)$