1. 5.3 Slopes of Straight Lines
Hubarth
Math 90

2. Ex 3 Finding the Slope Using a Graph
Finding Slope
Ex 3 Finding the Slope Using a Graph
Find the slope of each line. a.
slope =
rise
run
4 – 1
0 – 2 =
The slope of the line is – . 3 2 = 3 –2
= – 3 2 b.
slope =
rise
run
The slope of the line is 2.
–1 – 1
–2 – (–1) = = –2 –1
= 2

3. Ex 1 Finding Slope Using Points
Find the slope of the line through E(3, –2) and F(–2, –1).
slope =
y2 – y1
x2 – x1
Substitute (–2, –1) for (x2, y2) and
(3, –2) for (x1, y1).
–1 – (–2)
–2 – 3 =
= – 1 5 = –5
Simplify.
The slope of EF is – . 1 5

4. Ex 2 Horizontal and Vertical Lines
Find the slope of each line. a.
slope =
y2 – y1
x2 – x1
2 – 2
1 – (–4) =
Substitute (1, 2) for (x2, y2) and (–4, 2) for (x1, y1). = 5
Simplify.
The slope of the horizontal line is 0.
= 0
slope =
y2 – y1
x2 – x1 b.
Substitute (2, 1) for (x2, y2) and (2, –4) for (x1, y1). =
1 – (–4)
2 – 2 = 5
Simplify.
Division by zero is undefined.
The slope of the vertical line is undefined.

5. Summary
Slope of Lines
A line with a
Positive slope
slants upward
from left to right
A line with a
negative slope
slants downward
from left to right
A line with a
slope of 0 is
horizontal
A line with an
undefined slope is
vertical.
if the denominator is
0, then the slope is
undefined

6. Ex 3 Identifying Slope and Y-intercept
What are the slope and y-intercept of y = 2x – 3 then graph?
mx + b
y =
2x – 3
Use the Slope-Intercept form.
slope, m = 2
y-intercept, b = (0, -3)

7. Ex 4 Writing an Equations2 5
Write an equation of the line with slope and y-intercept 4 then graph.
Use the slope-intercept form.
y = mx + b
y = x + 4 2 5
Substitute for m and 4 for b.

8. . . Practice 1. Find the slope of a line passing through the points
a. (3, 4) and (-2, 3) b. (-2, 5) and (-3, 6)
𝑚= 1 5
𝑚= 1 −1 =−1
2. Find the slope from the given graphs. a. . b. c. .
(2, 2)
(-1, 0)
𝑚= 2 3
m=0
undefined
3. Find the slope and y-intercept of each equation and then graph.