2. The slope of a non-vertical line is the
ratio of the vertical change (the rise) to
the horizontal change (the run) between
any two points on the line.
vertical change change in y
=
horizontal change change in x
3. Example 1 Find the slope of the line shown.
Write formula for
slope.
y2 – y1
m=
x2 – x1
4. If you know any two points on a line, you
can find the slope of the line without
graphing. The slope of a line through the
points (x1, y1) and (x2, y2) is as follows:
rise y2 – y1
slope = =
run x2 – x 1
5. Example 1: Finding Slope, Given Two Points
Find the slope of the line that passes through
A. (–2, –3) and (4, 6).
Let (x1, y1) be (–2, –3) and (x2, y2) be (4, 6).
y2 – y1 6 – (–3) Substitute 6 for y2, –3 for y1,
x2 – x1 = 4 – (–2) 4 for x2, and –2 for x1.
= 6 + 3 =9
4+2 6
=3 Simplify.
2
3
The slope of the line is 2 .
6. Example 2: Finding Slope, Given Two Points
Find the slope of the line that passes through
B. (1, 3) and (2, 1).
Let (x1, y1) be (1, 3) and (x2, y2) be (2, 1).
y2 – y1 1 – 3 Substitute 1 for y2, 3 for y1,
x2 – x1 = 2 – 1 2 for x2, and 1 for x1.
= −2 = –2 Simplify.
1
The slope of the line that passes through
(1, 3) and (2, 1) is –2.
7. WARM UP
Find the slope of the line that passes through
C. (3, –2) and (1, –2).
Let (x1, y1) be (3, –2) and (x2, y2) be (1, –2).
y2 – y1 –2 – (–2) Substitute −2 for y2, −2 for y1,
x2 – x1 = 1 – 3 1 for x2, and 3 for x1.
= −2 + 2 Rewrite subtraction as addition of
1–3 the opposite.
0
= –2 = 0
The slope of the line that passes through
(3, –2) and (1, –2) is 0.
8. WARM UP
Find the slope of the line that passes through
A. (3, 5) and (3, 1).
Let (x1, y1) be (3, 5) and (x2, y2) be (3, 1).
9. Helpful Hint
You can use any two points to find the
slope of the line.
The slope of a line may be positive, negative,
zero, or undefined. You can tell which of these
is the case by looking at the graphs of a line—
you do not need to calculate the slope.
