Question

What is the equation in slope-intercept form for the line that passes through the point (8,-3) and has a nice of -2?

Answer 1

To find the slope of the line you can replace the information given in the general equation of the line in its slope-intercept form and solve for m, that is,

$\begin{gathered} y=mx+b \\ \text{ Where m is the slope of the line and} \\ b\text{ is the y-intercept} \end{gathered}$

So, you have

$\begin{gathered} (x,y)=(8,-3) \\ b=-2 \\ y=mx+b \\ \text{ Replacing} \\ -3=m\cdot8-2 \\ \text{ Solving for m} \\ -3=8m-2 \\ \text{ Add 2 from both sides of the equation} \\ -3+2=8m-2+2 \\ -1=8m \\ \text{ Divide by 8 into both sides of the equation} \\ \frac{-1}{8}=\frac{8m}{8} \\ \frac{-1}{8}=m \end{gathered}$

Then the slope of the line is

$m=-\frac{1}{8}$

Now, since you already have the slope and the y-intercept, you can know what the equation of the line is in its slope-intercept form

$\begin{gathered} y=mx+b \\ y=-\frac{1}{8}x-2 \end{gathered}$

Therefore, the equation in slope-intercept form for the line that passes through the point (8,-3) and has a y-intercept of -2 is

$y=-\frac{1}{8}x-2$

And the correct answer is A.