Name ________________________
4.4 Day 2 Notes
Find Slope and the Rate of Change
The slope of a nonvertical line is the ratio of the vertical change (the rise) to the
horizontal change (the run) between any two points on the line. The slope of the line is
represented by the letter m.
SLOPE = m =
y2 – y1
x2 – x1
rise = change in y =
run
change in x
y2 – y1
x 2 – x1
is the formula we use to find slope when we are given two
points (x1 , y1) and (x2,y2)
For example, if we want to find the slope of the line that passes through the points (2,4)
and (12, 8), we would plug the values into the formula, then simplify.
Vertical change (change in y’s)
8 – 4 which equals 4 which makes the slope
Horizontal change (change in x’s) 12 – 2
10
Which means that the line is going UP 2 and OVER 5 forever and ever!
Find the slope of the line through the following points:
1) (1, -1) and (2, -2)
4) (0,0) and (-9,-9)
2) (0,-5) and (-6, -9)
5)
(0,-9) and (0,9)
3) (-9, -9) and (0,0)
6) (9.0) and (-9,0)
2
5
Guided Practice
Find the slope of the line that goes through the following points using slope equation:
1) (1, -4) and (5, -8)
2) (-3,6) and (-3,0)
3) (-3,3) and (7,-1)
4) (0,-2) and (9,-5)
5) (7,1) and (-2,1)
6) (-3,-1) and (6,-2)
Find the value of x so that the line that passes through the points (2,3) and (x,9) has a
3
slope of . To do this, set up a proportion and solve.
2
3
= 9–3
3(x-2) = 2(9-3)
3x-6 = 12
x=6
2
x- 2
Try these on your own:
1. (-3,y) and (-9,-2); m=1
2. (-1,4) and (x,3); m =
Now you make up one and share with the class!!!!!
1
5
3. (8,1) and (1,y); -1