1. 12-5 Slope
Warm Up
Problem of the Day
Lesson Presentation
Course 2

2. 12-5 Slope
Learn to determine the slope of a line
and to graph a line, given one point, the
y-intercept, and the slope.
Course 2

3. 12-5 Slope Lesson Title Here
Insert
Vocabulary
slope
y-intercept
slope-intercept form
Course 2

4. 12-5 Slope
The slope of a line is a measure of its steepness
and is the ratio of rise to run:
y
Run
Rise
x
y-intercept
The y-coordinate of the point where a line crosses
the y-axis is called the y-intercept.
Course 2

5. 12-5 Slope
Additional Example 1A: Identifying Slope and
y-intercept of a line
A. Give the slope and y-intercept of the line.
3
3
y-intercept
The rise is 3. The run is 3.
slope = rise = 3 = 1
run 3
The y-intercept is –4.
Course 2

6. 12-5 Slope
Additional Example 1B: Identifying the Slope and
y-intercept of a Line
B. Give the slope and y-intercept of the line.
y-intercept
2
The rise is 0. The run is 2.
slope = rise = 0 = 0
run 2
The y-intercept is –1.
Course 2

7. 12-5 Insert Lesson Title Here
Slope
Try This: Example 1A
A. Give the slope and y-intercept of the line.
The rise is 0. The run is –8.
y-intercept slope = rise = 0 = 0
run –8
The y-intercept is –3.
–8
(–4, –3) (4, –3)
Course 2

8. 12-5 Insert Lesson Title Here
Slope
Try This: Example 1B
B. Give the slope and y-intercept of the line.
(–2, 4)
–4 The rise is 8. The run is –4.
8 y-intercept
slope = rise = 8 = –2
run –4
The y-intercept is 0.
(0, –4)
Course 2

9. 12-5 Slope
A linear equation with the variable y isolated on the
left-hand side of the equation is in slope-intercept
form.
y = mx + b
Slope y-intercept
Course 2

10. 12-5 Slope
Additional Example 2: Identifying Slope and
y-intercept in a Linear Equation
Give the slope and y-intercept of each line,
given the equation.
A. y = 3x – 1
y = 3x – 1
The slope is 3.
The y-intercept is –1.
B. y = 1 x + 2
2
y = 1x + 2
2
1.
The slope is 2
The y-intercept is 2.
Course 2

11. 12-5 Insert Lesson Title Here
Slope
Try This: Example 2
Give the slope and y-intercept of each line,
given the equation.
A. y = 4x – 4
y = 4x – 4
The slope is 4.
The y-intercept is –4.
1
B. y = 3 x + 3
y = 1x + 3
3
1.
The slope is 3
The y-intercept is 3.
Course 2

12. 12-5 Slope
When you know the slope and any one point
on a line, you can graph the line.
Course 2

13. 12-5 Slope
Additional Example 3: Graphing Linear Equations
Using Slope and y-intercept
Graph each line, given the equation.
A. y = –2x + 1
y = –2x + 1 (–1, 3)
2
The slope is –2 or –1
The y-intercept is 1.
From point (0, 1) move 2
units up (rise) and 1 unit
left (run) to find another
point on the line. Draw a
line to connect the points
Course 2

14. 12-5 Slope
Additional Example 3B: Graphing Linear Equations
Using Slope and y-intercept
Graph the line, given the equation.
B. y = 3
y = 0x + 3 (0, 3)
The slope is 0. The y-
intercept is 3.
Locate the point (0, 3).
When the slope is zero
the line is horizontal.
Draw a horizontal
line through point (0, 3).
Course 2

15. 12-5 Insert Lesson Title Here
Slope
Try This: Example 3A
Graph the line, given the equation.
A. y = x – 4
y = 1x – 4
The slope is 1.
The y-intercept is –4.
From point (0, –4) move 1
unit up (rise) and 1 unit
right (run) to find another (1, –3)
point on the line. Draw a (0, –4)
line to connect the points
Course 2

16. 12-5 Insert Lesson Title Here
Slope
Try This: Example 3B
Graph the line, given the equation.
B. y = –1
y = 0x – 1
The slope is 0. The y-
intercept is –1.
Locate the point (0, –1). (–3, –1) (0, –1)
When the slope is zero the
line is horizontal. Draw a
horizontal line through
point (0, –1).
Course 2

17. 12-5 Slope Lesson Title Here
Insert
Lesson Quiz: Part 1
Tell the slope and y-intercept of each line,
given the equation.
1. y = x – 5 1; –5
2. y = 3 x 3 ; 0
4 4
3. y = –2x + 7 –2; 7
Course 2

18. 12-5 Slope Lesson Title Here
Insert
Lesson Quiz: Part 2
4. Graph the line, given the equation y = 1x – 2.
2
Course 2