Question

Find the equation of the line that passes through the given point and has the given slope. Express your answer in slope-intercept form.1(3,0), m= -8

Answer 1

Given the word problem, we can deduce the following information:

1. Point (3,0)

2. m=-1/8

To find the slope-intercept form of the equation, we use the formula:

$y=mx+b$

where:

m=slope

b=y-intercept

First, we plug in x=3, y =0, and m=-1/8 into y=mx+b to find the value of b:

$\begin{gathered} y=mx+b \\ 0=-\frac{1}{8}(3)+b \\ \text{Simplify and rearrange} \\ b=\frac{3}{8} \end{gathered}$

Then, we plug in b=3/8 and m=-1/8 into the slope-intercept form formula:

$\begin{gathered} y=mx+b \\ y=-\frac{1}{8}x+\frac{3}{8} \end{gathered}$

Therefore, the answer is:

$y=-\frac{1}{8}x+\frac{3}{8}$