Chapter 8.3, Problem 25E

To determine

To find:

The intercepts of theequation’s graph. Then graph the equation.

Answer to Problem 25E

x -intercept: $(3,0)$

y -intercept: $(0,6)$

Explanation of Solution

Given:

An equation: $\frac{1}{2}x+\frac{1}{4}y=\frac{3}{2}$

Calculation:

To find x -intercept, we will substitute $y=0$ in our given equation and solve for xas shown below:

  $\begin{array}{l}\frac{1}{2}x+\frac{1}{4}y=\frac{3}{2}\left(\text{Given equation}\right)\\ \frac{1}{2}x+\frac{1}{4}(0)=\frac{3}{2}\left(\text{Substituting }y=0\right)\\ \frac{1}{2}x+0=\frac{3}{2}\\ \frac{1}{2}x=\frac{3}{2}\\ \frac{1}{2}\cdot 2\cdot x=\frac{3}{2}\cdot 2\left(\text{Multiplying both sides by }2\right)\\ x=3\end{array}$

Therefore, the x -intercept of our given equation is $(3,0)$ .

To find y- intercept, we will substitute $x=0$ in our given equation and solve for yas shown below:

  $\begin{array}{l}\frac{1}{2}x+\frac{1}{4}y=\frac{3}{2}\left(\text{Given equation}\right)\\ \frac{1}{2}(0)+\frac{1}{4}y=\frac{3}{2}\left(\text{Substituting }x=0\right)\\ \frac{1}{4}y=\frac{3}{2}\\ \frac{1}{4}\cdot 4\cdot y=\frac{3}{2}\cdot 4\left(\text{Multiplying both sides by 4}\right)\\ y=6\end{array}$

Therefore, the y -intercept of our given equation is $(0,6)$ .

Upon graphing our given equation, we will get our required graph as shown below: