Q. 93 - Precalculus Enhanced with Graphing Utilities

Question

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

(b) Graph the equation

$-4x+5y=40$

Step-by-Step Solution

Answer

(a)

x-intercept is $(-10,0)$

y-intercept is $(0,8)$

(b)

The graph is 

Step 1. Given information

The equation of a line is 

$-4x+5y=40$

Step 2. Finding the x-intercept

The equation of the line is 

$-4x+5y=40$

Plug $y=0$ and find x-value

$$\begin{gathered} -4x+5\times 0=40 \\ -4x+0=40 \\ -4x=40 \\ x=-10 \end{gathered}$$

So,

x-intercept is $(-10,0)$

Step 3. Finding the y-intercept

The equation of a line is 

$-4x+5y=40$

Plug $x=0$ and find y-value

$$\begin{gathered} -4\times 0+5y=40 \\ 0+5y=40 \\ 5y=40 \\ y=8 \end{gathered}$$

So, 

y-intercept is $(0,8)$

Step 4. Sketching the graph

Locate points $(-10,0),(0,8)$ on the graph and then join them to sketch the graph.