Chapter 1.3, Problem 5CFU

To determine

To graph: equation, $3x-4y+2=0$ using x- and y-intercepts.

Answer to Problem 5CFU

  

Explanation of Solution

Given information:

The equation is a follows:

  $3x-4y+2=0$ … (1)

Calculation:

To find the x-intercept, put $y=0$ in equation (1) and simplify it as follows:

  $\begin{array}{c}3x-4\left(0\right)+2=0\\ 3x-0+2=0\\ 3x+2=0\\ 3x=-2\\ x=-\frac{2}{3}\end{array}$

Thus, the coordinates of x-intercept is $\left(-\frac{2}{3},0\right)$ .

To find the y-intercept, put $x=0$ in equation (1) and simplify it as follows:

  $\begin{array}{c}3\left(0\right)-4y+2=0\\ 0-4y+2=0\\ -4y+2=0\\ 4y=2\\ y=\frac{2}{4}\\ y=\frac{1}{2}\end{array}$

Thus, the coordinates of y-intercept is $\left(0,\frac{1}{2}\right)$ .

Now, graph the coordinates $\left(-\frac{2}{3},0\right)$ and $\left(0,\frac{1}{2}\right)$ as shown below.