Question

For each description, write the equation of the line in point-slope form and in slope-intercept form.The line passes through the two points (4,-2) and (-8,1)

Answer 1

The point-slope form is as follows:

$y-y_P=m(x-x_P)$

Where m is the slope and (xP, yP) is a point on the line. We can use any opint as long as it is on the line.

The slope-intercept form is:

$y=mx+b$

Where m is the same slope and b is the y-intercept. We can find it by either using the y-intercept or by solving the slope-point form for y.

First, we need to find the slope using the points (4, -2) and (-8, 1):

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-(-2)}{-8-4}=\frac{1+2}{-12}=\frac{3}{-12}=-\frac{1}{4}$

So, to find the point-slope form, we can use either points, so let's use (4, -2):

$\begin{gathered} y-(-2)=-\frac{1}{4}(x-4) \\ y+2=-\frac{1}{4}(x-4) \end{gathered}$

And to find the slope-intercept, we just solve the parenthesis and solve for y:

$\begin{gathered} y+2=-\frac{1}{4}(x-4) \\ y+2=-\frac{1}{4}x+1 \\ y=-\frac{1}{4}x+1-2 \\ y=-\frac{1}{4}x-1 \end{gathered}$

So, one of the possible point-slope forms is:

$y+2=-\frac{1}{4}(x-4)$

And the slope-intercept form is:

$y=-\frac{1}{4}x-1$