1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Find the slope of the line that passes through each pair of points. ‏
Warm Up
Find the slope of the line that passes through each pair of points. ‏ 2 3
Negative; –

3. Problem of the Day
A cat weighs 11 ounces at birth. It gains 0.5 ounces a day for the first two weeks. How much will the cat weigh at the end of two weeks?
The cat will weigh 1 lb, 2 oz.

4. Learn to use slopes and intercepts to graph linear equations.

5. Vocabulary
x-intercept
y-intercept
slope-intercept form

6. The x-intercept of a line is the x- coordinate of the point where the line intersects the x-axis. The y-coordinate of this point is always 0.
The y-intercept of a line is the y-coordinate of the point where the line intersects the y-axis. The x-coordinate of this point is always 0.

7. Additional Example 1: Finding x-intercepts and
y-intercepts to Graph Linear Equations
Find the x-intercept and y-intercept. A. x y –2 –4 2 4
The line intersects the x-axis at (2,0).
The x-intercept is 2.
The line intersects the x-axis at (–4).
The y-intercept is –4.

8. Additional Example 1: Finding x-intercepts and
y-intercepts to Graph Linear Equations
Find the x-intercept and y-intercept. B. x y –2 –4 2 4
The line intersects the x-axis at (4,0).
The x-intercept is 4.
The line intersects the x-axis at (0, 1).
The y-intercept is 1.

9. Find the x-intercept and y-intercept. A.
Check It Out: Example 1
Find the x-intercept and y-intercept. A. x y –2 –4 2 4
The line intersects the x-axis at (1,0).
The x-intercept is 1.
The line intersects the x-axis at (–3).
The y-intercept is –3.

10. Find the x-intercept and y-intercept. B.
Check It Out: Example 1
Find the x-intercept and y-intercept. B. x y –2 –4 2 4
The line intersects the x-axis at (5,0).
The x-intercept is 5.
The line intersects the x-axis at (0, 2).
The y-intercept is 2.

11. The linear equation y = mx + b is written in slope-intercept form, where m is the slope and b is the y-intercept of the line.
y = mx + b
Slope
y-intercept

12. Additional Example 2A: Graphing by Using Slope
and y-intercept
Graph the equation.
y = x + 1
1 3
Step 1: Find m and b.
y = x + 1
1 3
m =
1 3
b = 1
Step 2: Plot (0, 1)‏
1 3
Step 3: Use the slope to plot at least 1 more point on the line.

13. Additional Example 2A Continued
Graph the equation.
y = x + 1
1 3 x y –2 –4 2 4
Step 4: Draw a line through the points.

14. Since the y-intercept is 1, the point (0, 1) is a point on the line.
Remember!

15. Additional Example 2: Graphing by Using Slope
and y-intercept
Graph the equation.
B. 3x + y = 5
Step 1: Find m and b.
3x + y = 5
– 3x = – 3x
y = 5 – 3x
y = –3x + 5
m = – b = 5

16. Additional Example 2B Continued
Step 2: Plot (0, 5)‏
Step 3: Use the slope –3 to plot at least 1 more point on the line.
Step 4: Draw a line through the points.

17. Check It Out: Example 2A
Graph the equation.
y = x + 2
1 4
Step 1: Find m and b.
y = x + 2
1 4
m =
1 4
b = 2
Step 2: Plot (0, 2)‏
1 4
Step 3: Use the slope to plot at least 1 more point on the line.
Step 4: Draw a line through the points.

18. Check It Out: Example 2A Continued
Graph the equation.
y = x + 2
1 4 x y –2 –4 2 4
Step 4: Draw a line through the points.

19. Check It Out: Example 2B
Graph the equation.
2x + y = 4
Step 1: Find m and b.
2x + y = 4
– 2x = – 2x
y = 4 – 2x
y = –2x + 4
m = – b = 4

20. Check It Out Example 2B Continued
Step 2: Plot (0, 4)‏
Step 3: Use the slope –2 to plot at least 1 more point on the line.
Step 4: Draw a line through the points.

21. Additional Example 3: Writing an Equation in Slope-Intercept Form
Write the equation of the line in slope-intercept form.
The line rises from right to left so the slope is negative.
m =
rise
run
= - 2 5
The line intersects the y-axis
at (0, -4), so the y-intercept
is -4.
b = –4
Substitute for m and b.
y = 2 5
x – 4

22. Check It Out: Example 3
Write the equation of the line in slope-intercept form.
The line rises from left to right so the slope is positive.
m =
rise
run = 1 2
The line intersects the y-axis
at (0, 2), so the y-intercept
is 2.
b = 2
Substitute for m and b.
y = 1 2
x + 2

23. Additional Example 4: Using Slope-Intercept Form
A spider descends a 20-foot drainpipe at a rate of 2 feet per minute. The linear equation y = –2x + 20 represents the distance y the spider has left to descend after x minutes. Graph the equation, and then identify the x- and y- intercepts and describe their meaning.

24. Additional Example 4 Continued
Spider's Decent
Use the slope and y-intercept to graph the equation. 20 18
Plot (0, 20). Use the slope -2 to plot the line down to the x-axis. 16 14 12
The y-intercept is 20. This represents the total distance in feet the spider has to descend.
Distance remaining (ft)‏ 10 8 6 4
The x-intercept is 10. This represents the time in minutes it takes the spider has to descend the 20 ft. 2 2 4 6 8 10 12 14 16
Time (min)‏

25. Check It Out: Example 4
A submarine descends into a 40-mile sea cave at a rate of 5 miles per minute. The linear equation y = –5x + 40 represents the distance y the submarine has left to descend after x minutes. Graph the equation, and then identify the x- and y- intercepts and describe their meaning.

26. Check It Out: Example 4 Continued
Use the slope and y-intercept to graph the equation.
Submarine's Decent 45
Plot (0, 40). Use the slope -5 to plot the line down to the x-axis. 40 35
Distance remaining (mi)‏ 30
The y-intercept is 40. This represents the total distance in feet the submarine has to descend. 25 20 15 10
The x-intercept is 8. This represents the time in minutes it takes the submarine to descend the 40 miles. 5 1 2 3 4 5 6 7 8 9
Time (min)‏

27. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

28. 1. Graph y = x – 3. Identify the x- and y- intercepts. 3 8
Lesson Quiz: Part I
1. Graph y = x – 3. Identify the x- and y- intercepts.
3 8 x y –4 –8 4 8
x-int. = 8, y-int. = –3

29. 2. Write the equation of the line in slope- intercept form.
Lesson Quiz: Part II
2. Write the equation of the line in slope- intercept form. x y –4 –8 4 8
y = – x + 3
1 2

30. Lesson Quiz
3. A snail is crawling across a 15 mm long leaf. The snail crawls at a constant rate of 1 mm per second. The linear equation y = –x + 15 represents the distance y that the snail has left to crawl after x seconds. Graph the equation, and then identify the x- and y-intercepts and describe their meanings.
y-int. = 15, total distance in mm that the snail has to crawl;
x-int. = 15, time in seconds it takes the snail to crawl 15 mm.

31. Lesson Quiz for Student Response Systems
3 2
Graph y = – x – 3. Identify the x- and
y-intercepts.
A. x-int: –2, y-int: –3 B. x-int: 2, y-int: 3

32. Lesson Quiz for Student Response Systems
2. Write the equation of the line in slope-intercept form.
A. y = x – 3
B. y = x + 2
C. y = x – 3
D. y = x + 2
2 3
2 3
3 2
3 2

33. Lesson Quiz for Student Response Systems
3. A gelato shop charges $3 for a cup of gelato, plus $1.50 for each topping. The equation C = 1.5t + 3 represents the cost of the cup of gelato for t number of toppings. Graph the equation, and then identify the x- and y-intercepts.
A. x-int: 3, y-int: none B. x-int: none, y-int: 3