Q. 19 - Precalculus Enhanced with Graphing Utilities

Question

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

$2x+3y=6$.

Step-by-Step Solution

Answer

The intercepts are :

x-intercept is $\left(3,0\right)$ and y-intercept is $\left(0,2\right)$.

Step 1: Given information:

Consider the equation,

$2x+3y=6$.

Step 2: To find the x-intercept:

Let $y=0$ in the equation,

Then, $2x+3\times 0=6$

$2x=6$

$\frac{2x}{2}=\frac{6}{2}$

$x=3$

$x-intercept is (3,0).$

Step 3: To find the y-intercept:

Let $x=0$ in the equation,

Then, $2\times 0+3y=6$

$3y=6$

$\frac{3y}{3}=\frac{6}{3}$

$y=2$

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

Step 4: To draw the graph:

We can draw the graph of the equation $2x+3y=6$ by plotting the above intercepts and the points in the table below,

$x$	$y=\frac{6-2x}{3}$	$\left(x,y\right)$
$-2$	$\frac{10}{3}$	$\left(-2,\frac{10}{3}\right)$
$-1$	$\frac{8}{3}$	$\left(-1,\frac{8}{3}\right)$
$1$	$\frac{4}{3}$	$\left(1,\frac{4}{3}\right)$
$2$	$\frac{2}{3}$	$\left(2,\frac{2}{3}\right)$