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

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!

• 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!

• 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!

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.

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

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!

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!

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.

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

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. • •

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. • •

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

• • 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.

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

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

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

• • 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.

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!

• Remember standard form for a linear equation: Graph x = -3 y 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.

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.

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

• • 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?

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

Homework Pg.159-161 #18-23;30-32;36-37;45,49,50,55,61,63. Algebra rocks!