1. 3-3B Linear Functions Graphing using Intercepts
Algebra Glencoe McGraw-Hill Linda Stamper

2. An x-intercept is the x-coordinate of a point where a graph crosses the x-axis.
A y-intercept is the y-coordinate of a point where a graph crosses the y-axis. y
coordinate (0,–4)
y-intercept is –4 • x
coordinate is (3,0)
x-intercept is 3 •
The x-intercept and the y-intercept are numerical values. They are NOT ordered pairs!

3. • Example 1 Use the graph to find the x-intercept of the line.y
1. Locate the x-intercept.
2. Identify the coordinate. • x
(–2,0) –2
3. Name the x-intercept.
The x-intercept is a numerical value. It is NOT an ordered pair!

4. • Example 2 Use the graph to find the y-intercept of the line.
1. Locate the y-intercept.
2. Identify the coordinate. x
(0,–3) –3 •
3. Name the y-intercept.
The y-intercept is a numerical value. It is NOT an ordered pair!

5. Do not write x = 4 or y = -4. The answers are NOT equations.
Example 3 Use the graph to find the x-intercept and the y-intercept of the line. y
Name the x-intercept.
x-intercept is 4 •
Name the y-intercept. x
y-intercept is –4 •
Do not write x = 4 or y = -4. The answers are NOT equations.

6. Not all intercepts are integers.
Can you use the graph to find the x-intercept and the y-intercept of the line? y
Not all intercepts are integers. i
Some of your homework problems will give you the equation of the line and not the graph. Given an equation, you can find the intercepts. x

7. Find the x-intercept of the graph of equation 8x – 5y = 2.
Write equation.
Substitute zero for y because at the x-intercept the y-coordinate is zero.
Solve for x.
Name the intercept.
When finding the x-intercept, solve the equation for x. The answer is a numerical value – not an equation!

8. Find the y-intercept of the graph of equation 3x – 6y = 18.
Write equation.
Substitute zero for x because at the y-intercept the x-coordinate is zero.
Solve for y.
Name the intercept.
When finding the y-intercept, solve the equation for y. The answer is a numerical value – NOT an equation!

9. Example 4 Find the x-intercept and the y-intercept of the graph of equation 5x + 2y = 20
Write equation.
Write equation.
Find the y-intercept.
(Solve the equation for y.)
Find the x-intercept.
(Solve the equation for x.)
Name the y-intercept.
Name the x-intercept.

10. Example 5 Find the x-intercept and the y-intercept of the graph of equation 3x – 4y = 12

11. In the previous lesson you learned to graph an equation using a table of values.
In this lesson you will learn how to make a quick graph using the intercepts. The Quick Graph process works because only two points are needed to determine a line. • •

12. In the previous lesson you learned to graph an equation using a table of values.
In this lesson you will learn how to make a quick graph using the intercepts. The Quick Graph process works because only two points are needed to determine a line. • •

13. In the previous lesson you learned to graph an equation using a table of values.
In this lesson you will learn how to make a quick graph using the intercepts. The Quick Graph process works because only two points are needed to determine a line. • •

14. Making a Quick Graph 1. Find the intercepts.
2. Draw a coordinate plane that includes the intercepts.
3. Plot the intercepts and draw a line through them.
How many solutions are there to an equation in x and y?
infinitely many solutions

15. • • Graph the equation 2x + 5y = –10 using intercepts. Write equation.
Find the x-intercept • x
Write equation. •
Find the y-intercept y
Draw a coordinate plane that includes (–5,0) and (0,–2).
Plot the coordinates for the x-intercept and y-intercept.
Draw a line through the points.

16. Graph each equation using intercepts.
Example 6 3x – 4y = 12
Example 7 3x + 2y = 12
Example 8 y = 4x + 40

17. Example 6 Graph 3x – 4y = 12 using intercepts.• x • y

18. Example 7 Graph 3x + 2y = 12 using intercepts.• • x y

19. • • Example 8 Graph y = 4x + 40 using intercepts.20 • x
–20 20
–20 y
Find an appropriate scale that includes points (–10,0) and (0,40). Use the same scale on both axis.

20. Will all equations have an x-intercept and a y-intercept?
Vertical lines will only have an x-intercept.
Horizontal lines will only have a y-intercept.
You can graph a line using one point, if you know it is a vertical or horizontal line! How can you tell by looking at the equation?
Horizontal and vertical lines have only one variable in the equation!

21. • Remember standard form for a linear equation: Graph x = -3y
This is why you could not write the x-intercept as an equation
x=-3. • x
When “B” is equal to zero you will have an equation with one variable.
x = -3 is the graph of a vertical line.

22. When “A” is equal to zero you will have an equation with one variable.
Graph y = -3
When “A” is equal to zero you will have an equation with one variable. x • y
y = -3 is the graph of a horizontal line.

23. Example 9 Graph x = 4.
Example 10 Graph x = –2.
Example 11 Graph y = 4.
Example 12 Graph y = –2.

24. • • Example 9 Graph x = 4. Example 10 Graph x = –2. x x y y
How did you know by looking at the equation that it would NOT graph as a diagonal line?

25. Example 11 Graph y = 4.
Example 12 Graph y = –2. • x x • y y

26. Homework Pg
#18-23;30-32;36-37;45,49,50,55,61,63.
Algebra rocks!