Question

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

$y=3x-9$.

Short answer

The intercepts are :

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

Step-by-step solution

Given information:

Consider the equation,

$y=3x-9$.

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. ]

$x=3$

localid="1646398491531" $x-interceptis\left(3,0\right).$

To find the y-intercept:

Let $x=0$in the equation,

Then $y=3\times 0-9$

$y=-9$

localid="1646398539079" $y-interceptis\left(0,-9\right).$

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	$\left(2,-3\right)$