Chapter B, Problem 18E

Find an equation of the line that satisfies the given conditions.

30. x-intercept −8, y-intercept 6

To determine

To find: The equation of the line for the given conditions.

Answer to Problem 18E

The equation of the line is $y=\frac{3}{4}x-6$.

Explanation of Solution

Given:

The required is passing through $x\text{ intercept }-8$ and $y\text{ intercept 6}$.

Property used:

The equation of the line passes through the point $\left(x_1,y_1\right)$ and having slope m is, $y-y_1=m\left(x-x_1\right)$.

The equation of the line with slope $m$ and $y\text{ intercept }b\text{ is}$, $y=mx+b$.

Calculation:

To find the slope, solve the equation, consider the intercepts as points $\left(1,0\right)\text{ and }\left(0,-3\right)$

$\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ 6-0=m\left(0-\left(-8\right)\right)\\ \frac{6}{8}=m\\ \frac{3}{4}=m\end{array}$

Therefore, $m=\frac{3}{4}$.

Substitute the values in the property mentioned above.

$\begin{array}{l}m=\frac{3}{4},b\text{=6}\\ \text{Therefore,}\\ y=\frac{3}{4}x-6\end{array}$

Thus, the equation of the line is $y=\frac{3}{4}x-6$.