Q. 91 - Precalculus Enhanced with Graphing Utilities

Question

(a) Find the intercepts of the graph of the equation

(b) Graph the equation

$2x+3y=6$

Step-by-Step Solution

Answer

(a)

x-intercept is $(3,0)$

y-intercept is $(0,2)$

(b)

The graph is 

Step 1. Given information

The equation of a line is 

$2x+3y=6$

Step 2. Finding the x-intercept

The equation of the line is 

$2x+3y=6$

Plug $y=0$ and find x-value

$$\begin{gathered} 2x+3\times 0=6 \\ 2x+0=6 \\ 2x=6 \\ x=\frac{6}{2}=3 \end{gathered}$$

So, 

x-intercept is $(3,0)$

Step 2. Finding the y-intercept

The equation of a line is 

$2x+3y=6$

Plug $x=0$ and find y-value

$$\begin{gathered} 2\times 0+3y=6 \\ 0+3y=6 \\ 3y=6 \\ y=2 \end{gathered}$$

So, 

y-intercept is $(0,2)$

Step 4. Sketching the graph

Locate intercept points $(3,0),(0,2)$ on the graph and then join them to sketch the graph.