Question

A line contains the points (3, –2) and (–6, –8). Write the equation of the line using point-slope form.

Answer 1

(3,-2)(-6,-8)
slope = (-8 - (-2) / (-6 - 3) = (-8 + 2) / -9 = -6 / -9 = 2/3

y - y1 = m(x - x1).....there are 2 possible answers for this
slope(m) = 2/3
using points (3,-2)
now we sub...pay close attention to ur signs
y - (-2) = 2/3(x - 3) =
y + 2 = 2/3(x - 3) <== here is one possible answer

y - y1 = m(x - x1)
slope(m) = 2/3
using points (-6,-8)
now we sub
y - (-8) = 2/3(x - (-6) =
y + 8 = 2/3(x + 6) <=== here is the other possible answer

Answer 2

Let the coordinates of A be (3, -2) and B (-6, -8).
The general formula of the point-slope form is y - y1 = m(x - x1), in which m is the slope, x and y the coordinates of a point, x1 and y1 know coordinates.
First, we need to find the slope m of the line.
m = (yB - yA) / (xB - xA) = (-8 + 2) / (-6 - 3) = -6 / -9 = 2/3

So now we have: y - y1 = 2/3 (x - x1)

As we stated before, x1 and y1 are known coordinates of a point. By hypothesis, we have 2 points, so 2 possible choices:

1) For A (3, -2) in which x1 = 3 and y1 = -2
y - (-2) = 2/3 (x - 3)
y + 2 = 2/3 (x-3)

2)For B (-6, -8) in which x1 = -6 and y1 = -8
y - (-8) = 2/3 (x - (-6) )
y + 8 = 2/3 (x+6)

So the point-slope form of this line is:
y + 2 = 2/3 (x-3) or y+8 = 2/3 (x+6)

I represented the graphic of the line at the end of my answer :)

Hope this Helps! :D