Q. 97 - Precalculus Enhanced with Graphing Utilities

Question

$\frac{1}{2}x+\frac{1}{3}y=1$

(a) find the intercepts of the graph of equation 

(b) graph the equation.

Step-by-Step Solution

Answer

Part (a) x-intercept: 2; y-intercept: 3

Part (b) Graph of the equation, $\frac{1}{2}x+\frac{1}{3}y=1$

Part (a) Step 1. Given information

Equation of a line: $\frac{1}{2}x+\frac{1}{3}y=1$

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

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

$\frac{1}{2}x+\frac{1}{3}\left(0\right)=1$

$\frac{1}{2}x+0=1$

$\frac{1}{2}x=1$

$x=2$

Part (a) Step 3. Finding y-intercept

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

$\frac{1}{2}\left(0\right)+\frac{1}{3}y=1$

$0+\frac{1}{3}y=1$

$\frac{y}{3}=1$

$y=3$

Part (b) Step 1. Graphing the equation

Graphing the equation, using the intercepts found above: