Q. 14 - Precalculus Enhanced with Graphing Utilities

Question

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

$y=3x-9$.

Step-by-Step Solution

Answer

The intercepts are :

x-intercept is $\left(3, 0\right)$ and y-intercept is $\left(0, -9\right)$

Step 1: Given information:

Consider the equation,

$y=3x-9$.

Step 2: To find the x-intercept:

Let $y=0$ in the equation,

Then $0=3x-9$

    $0+9=3x-9+9$  [ Add 9 on both sides. ]

          $9=3x$

      $\frac{3x}{3}=\frac{9}{3}$  [ Divide by 3 on both sides. ]

          $x=3$

$x-intercept is \left(3, 0\right).$

Step 3: To find the y-intercept:

Let $x=0$ in the equation,

Then $y=3\times 0-9$

   $y=-9$

$y-intercept is \left(0, -9\right).$

Step 4: To draw the graph:

We can draw the graph of the equation $y=3x-9$ by plotting the above intercepts and the points in the table below,

x	$y=3x-9$	$\left(x,y\right)$
-1	-12	$\left(-1,-12\right)$
1	-6	$\left(1,-6\right)$
2	-3	$\left(2,-3\right)$