Q. 98 - Precalculus Enhanced with Graphing Utilities

Question

$x-\frac{2}{3}y=4$

(a) find the intercepts of the graph of equation

(b) graph the equation.

Step-by-Step Solution

Answer

Part (a) x-intercept: 4; y-intercept: $-6$

Part (b) Graph of the equation, $x-\frac{2}{3}y=4$

Part (a) Step 1. Given information

Equation of a line: $x-\frac{2}{3}y=4$

Part (a) Step 2. Finding the x-intercept

To find the x-intercept, put $y=0$

$x-\frac{2}{3}\left(0\right)=4$

$x-0=4$

$x=4$

Part (a) Step 3. Finding y-intercept

To find the y-intercept, put $x=0$

$0-\frac{2}{3}y=4$

$-\frac{2}{3}y=4$

$y=-\frac{3\times 4}{2}$

$y=-6$

Part (b) Step 1. Graphing the equation

Graphing the equation, using the intercepts found above: