Chapter 3.4, Problem 21E

To determine

To graph the linear equation:

$-\frac{5}{2}x+y=10$

Using intercepts, and also label the points corresponding to intercepts.

Answer to Problem 21E

Explanation of Solution

Given:

$-\frac{5}{2}x+y=10$

Concept Used:

• To graph a linear equation $ax+by=c$:
1. Find x and y intercepts.
2. Plot the points obtained in above step.
3. Draw a line through these points.
• To find x -intercept of graph of a equation put $y=0$ in the equation and solve for x .
• To find y -intercept of graph of a equation put $x=0$ in the equation and solve for y .

Calculation:

In order to graph the linear equation:

$-\frac{5}{2}x+y=10$

First, find it’s intercepts. For x -intercept of equation put $y=0$ in the equation and solve for x. As,

$\begin{array}{c}-\frac{5}{2}x+0=10\\ \Rightarrow -\frac{5}{2}x=10\\ \Rightarrow -5x=10\times 2\\ \Rightarrow x=\frac{20}{-5}\\ \Rightarrow x=-4\end{array}$

Thus, x -intercept is: $\left(-4,0\right)$ .

And for y -intercept of equation put $x=0$ in the equation and solve for $y$ . As,

$\begin{array}{c}-\frac{5}{2}\left(0\right)+y=10\\ \Rightarrow 0+y=10\\ \Rightarrow y=10\end{array}$

Thus, y -intercept is: $\left(0,10\right)$ .

Now finally to draw the graph of given linear equation, plot these ordered pairs, $\left(-4,0\right)$ and $\left(0,10\right)$ using a graphing utility and draw a line through them. The graph is represented as: