1. 2-3 Slope Slope indicates the steepness of a line.
is “the change in y over the change in x” (vertical over horizontal).
is the ‘m’ in y = mx + b.

2. Finding the Slope of a Line
m = m
We use the first equation when given a graph, the second when given a table, and the third when given two points.

3. Slope If a line rises from left to right (uphill),x y
If a line rises from
left to right (uphill),
it has a positive slope.
If a line falls from
left to right (downhill),
it has a negative slope. x y

4. Slope If a line is vertical, it has an undefined slope.
If a line is horizontal it has
a slope equal to 0. x y x y

5. Find the Slope To find the slope of this line we will use rise/run.
Pick either point.
We find the rise by
counting up (+) or down (-).
Rise is 3 up from the bottom or -3 down from the top point. y x

6. Find the Slope To find the run, we count right (+) or left (-).
If you started from the
top point, your run will be left
-2, if you started at the bottom
point, your run will be right 2. x y

7. Find the Slope So if you started with the top point, yourx y
So if you started with
the top point, your
slope would be -3/-2.
If you started with the bottom
point, your slope would be 3/2.
Are these the same? Yes!! The
slope of the line is 3/2.

8. Find the Slope x y x y
m =
m =

9. Find the Slope x y x y
m= undefined
m = 0

10. Find the Slope of the Line
Given the points (5, 1) & (6, 4)
m =
= = 3
Given the points (-6, -2) & (-1, 0)
m =

11. Slope-Intercept Form
y = mx + b [or f(x) = mx + b]
m is the slope
b is the y-intercept

12. Find the Equation of the Line
What is the
y-intercept?
b = -2
What is m?
m =
y = x -2 x y

13. Find the Equation of the Line
b = ?
b = 1
m = ?
m = -
y = - x + 1 x y

14. Find the Equation of the Line
b = ?
b = 4
m = ?
m = 0
y = 0x+4
y=4 x y

15. Find the Equation Given the Slope and y-intercept
1) m = -3, b = 1
y = -3x + 1
2) m = - , b = -4
y = - x - 4

16. Find the Slope and y-intercept of each Equation:
1) y = -4x + 3
m = -4
b = 3
2) y = x
m = -
b = 5
3) 8x + y =
m = -8
b =
4) 4x - 2y = 10
m = 2
b = -5

17. Find the Equation Given the Slope and a Point
Given m = -1, (2, 1)
First, calculate b by substituting the slope and the coordinates into y = mx + b.
y = -1x + b
1 = -1(2) + b
1 = -2 + b
3 = b
y = -1x + 3

18. Find the Equation Given Two Points
Given (-1, 3) and (2, 1)
First, calculate the slope:
Second, find b. Use either point...
m = , (2, 1)
1 = (2) + b
1 = b
= b

19. Homework:
Graphing Linear Equations Worksheet (front and back)