Q. 94 - Precalculus Enhanced with Graphing Utilities

Question

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

(b) Graph the equation

$6x-4y=24$

Step-by-Step Solution

Answer

(a)

x-intercept is $(4,0)$

y-intercept is $(0,-6)$

(b)

The graph is 

Step 1. Given information

The equation of a line is 

$6x-4y=24$

Step 2. Finding the x-intercept

The equation of the line is 

$6x-4y=24$

Plug $y=0$ and find x-value

$$\begin{gathered} 6x-4\times 0=24 \\ 6x-0=24 \\ 6x=24 \\ x=4 \end{gathered}$$

So,

x-intercept is $(4,0)$

Step 3. Finding the y-intercept

The equation of a line is 

$6x-4y=24$

Plug $x=0$ and find y-value

$$\begin{gathered} 6\times 0-4y=24 \\ 0-4y=24 \\ -4y=24 \\ y=-6 \end{gathered}$$

So,

y-intercept is $(0,-6)$

Step 4. Sketching the graph

Locate points $(4,0),(0,-6)$ on the graph and then join them to sketch the graph.