Chapter 8, Problem 5CT

To determine

To find:

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

Answer to Problem 5CT

x-intercept:

  $(4,0)$

y-intercept:

  $(0,4)$

Explanation of Solution

Given:

An equation:

  $x+y=4$

Calculation:

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

  $\begin{array}{l}x+y=4\left(\text{Given equation}\right)\\ x+0=4\left(\text{Substituting }y=0\right)\\ x=4\end{array}$

Therefore, the x-intercept of our given equation is $(4,0)$ .

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

  $\begin{array}{l}4x+3y=12\left(\text{Given equation}\right)\\ 4(0)+3y=12\left(\text{Substituting }x=0\right)\\ 0+3y=12\\ 3y=12\\ \frac{3y}{3}=\frac{12}{3}\\ y=4\end{array}$

Therefore, the y-intercept of our given equation is $(0,4)$ .

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