Q. 92 - Precalculus Enhanced with Graphing Utilities

Question

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

(b) Graph the equation

$3x-2y=6$

Step-by-Step Solution

Answer

(a)

x-intercept is $(2,0)$

y-intercept is $(0,-3)$

(b)

Step 1. Given information

The equation of a line is 

$3x-2y=6$

Step 2. Finding the x-intercept

The equation of the line is 

$3x-2y=6$

Plug $y=0$ and find y-value

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

So, 

x-intercept is $(2,0)$

Step 3. Finding the y-intercept

The equation of a line is 

$3x-2y=6$

Plug $x=0$ and find y-value

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

So, 

y-intercept is $(0,-3)$

Step 4. Sketching the graph

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