Q. 12 - Precalculus Enhanced with Graphing Utilities

Question

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

$y=x-6$.

Step-by-Step Solution

Answer

The intercepts are :

x-intercept is $\left(6, 0\right)$ and y-intercept is $\left(0, -6\right)$

Step 1: Given information:

Consider the equation,

$y=x-6$

Step 2: To find the x-intercept:

Let $y=0$ in the equation,

Then $0=x-6$

    $0+6=x-6+6$ [ add 6 on both sides. ]

           $6=x$

The solution is $x=6.$

$x-intercept is \left(6, 0\right).$

Step 3: To find the y-intercept:

Let $x=0$ in the equation,

Then $y=0-6$

          $y=-6$

$y-intercept is \left(0, -6\right).$

Step 4: To draw the graph:

We can draw the graph of the equation $y=x-6$ by plotting the above intercepts and the points in the table below,

x	$y=x-6$	$\left(x,y\right)$
4	-2	$\left(4,-2\right)$
2	-4	$\left(2,-4\right)$
-2	-8	$\left(-2,-8\right)$
-4	-10	$\left(-4,-10\right)$