3-3E Linear Functions Graphing using Intercepts Algebra 1 Glencoe McGraw-HillLinda Stamper

A y-intercept is the y-coordinate of a point where a graph crosses the y-axis. An x-intercept is the x-coordinate of a point where a graph crosses the x-axis. x y coordinate is (3,0) x-intercept is 3 coordinate (0,–4) y-intercept is –4 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. x y 1. Locate the x-intercept. 2. Identify the coordinate. (–2,0) 3. Name the x-intercept. –2 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. x y 2. Identify the coordinate. (0,–3) 3. Name the y-intercept. –3 1. Locate the y-intercept. The y-intercept is a numerical value. It is NOT an ordered pair!

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

Can you use the graph to find the x-intercept and the y-intercept of the line? i x y Not all intercepts are integers. 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.

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

Substitute zero for x because at the y-intercept the x-coordinate is zero. Find the y-intercept of the graph of equation 3x – 6y = 18. Write equation. 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. Find the x-intercept. (Solve the equation for x.) Name the x-intercept. Write equation. Find the y-intercept. (Solve the equation for y.) Name the y-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 Write equation. Find the y- intercept 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. x y

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. Find an appropriate scale that includes points (–10,0) and (0,40). Use the same scale on both axis. 20 –20 x y

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!

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

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

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

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

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

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