Find the slope of the line through P and Q. P(−8, 1), Q(5, −4)

Question

1.10 Lines

Answer 1

The two points are P(−8, 1) and Q(5, −4).

The formula for the slope between those two points is slope = (y2-y1)/(x2-x1).

slope = (1--4) / (-8-5) = 5/-13 = -5/13

Note that the order in which you take your points does not matter. You just need to be consistent regarding which coordinates you take as first, and which as second. I'm going to calculate it "in reverse" just now:

slope = (-4-1)/(5--8) = -5/13

You get the same result irrespective of whether you're talking P or Q as your first point and the other one as your second point.

Do pay attention to the minus sings. It is easy to forget a minus sign when a value is put into x1 or y1. If these numbers are negative in your point, then they become positive in the equation because you're doing "minus minus."

Answer 2

slope = (y2 - y1)/(x2 - x1)

Given that point P(-8,1) is our (x1,y1) and that point Q(5,-4) is our (x2,y2), then

the slope of the line through points P and Q is calculated as: (-4 -1)/(5 - -8) = -5/13

Answer 3

Visually speaking, in the formula, you're looking for what changes between the two points. If I start at P and go to Q, I change horizontally 13 points because my x goes from -8 to +5. This is my "run." Then on that same move, I go down 5 points because y goes from 1 to -4; this is my "rise" (a negative 5 because the opposite of rising/going up is falling/going down). Then, my slope is a ratio of those changes which is often called "rise over run;" in this case that's -5/13.

Answer 4

slope =(1+4)/(-8-5)= -5/13