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

2. 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.

3. Additional Example 1: Finding x- and
y-intercepts
Find the x- and y-intercepts. 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.

4. Additional Example 1: Finding x-intercepts and
y-intercepts to Graph Linear Equations
Find the x- and y-intercepts. 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.

5. Find the x- and y-intercepts. A.
Check It Out: Example 1
Find the x- and y-intercepts. 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.

6. Find the x- and y-intercepts. B.
Check It Out: Example 1
Find the x- and y-intercepts. 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.

7. 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

8. Additional Example 2A: Graphing by Using Slope
and y-intercept
Graph the equation.
A. 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)
Step 3: Use the slope to plot at least 1 more point on the line.
1 3

9. 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.

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

11. 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 is not in the form y = mx+b, so solve for y.
3x + y = 5
– 3x = – 3x
y = 5 – 3x
y = –3x + 5
m = – b = 5

12. 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.

13. 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)
Step 3: Use the slope to plot at least 1 more point on the line.
1 4

14. 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.

15. Check It Out: Example 2B
Graph the equation.
2x + y = 4
Step 1: Find m and b.
2x + y = 4 is not in the form y = mx+b, so solve for y.
2x + y = 4
– 2x = – 2x
y = 4 – 2x
y = –2x + 4
m = – b = 4

16. 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.

17. Additional Example 3: Writing an Equation in Slope-Intercept Form
Write the equation of the line in slope-intercept form.
The line falls from left to right 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

18. 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

19. 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.

20. 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
Distance remaining (ft)
The y-intercept is 20. This represents the total distance in feet the spider has to descend. 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)

21. 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.

22. 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)

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

24. 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

25. 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.