Chapter 13, Problem 6CT

To determine

To write an equation of the line with y-intercept 5 and x-intercept 3.

Answer to Problem 6CT

The equation of the line is $5x+3y=15$ .

Explanation of Solution

Given information :

The line intersects at $\text{(0, 5)}$ and $\text{(3, 0)}$

The slope of the line = $\frac{y-y_1}{x-x_1}$

  $\begin{array}{l}\frac{y-y_1}{x-x_1}=m\\ (x_1,y_1)=(0,5)\\ \frac{y-5}{x-0}=\frac{0-5}{3-0}\\ \frac{y-5}{x}=-\frac{5}{3}\\ 3(y-5)=-5x\\ 5x+3y=15\end{array}$

Hence,

The equation of the line is $5x+3y=15$ .