Algebra 1 November 11, 2013

1. Algebra 1November 11, 2013 4.3 Quick Graphs Using Intercepts

2. Objective Students will graph a linear equation using the x and y-intercepts

3. Before we begin… • In the previous lesson we graphed a linear equation by creating a table of values… • That is not the only way to graph a linear equation… • In this lesson we will look at graphing a linear equation using the x and y-intercepts…that is where the line crosses the x and y-axes

4. What does it mean to INTERCEPT a pass in football? The path of the defender crosses the path of the thrown football. In algebra, what are x- and y-intercepts?

5. Intercepts • Intercepts are key points to plot when graphing an equation. Remember, an intercepts is a POINT (x,y), and not just a number! • Look at the x-axis: What is true of EVERY point on the axis? (y-value is always 0) • Look at the y-axis: What is true of EVERY point on the axis? (x-value is always 0)

6. X-Intercepts • The x-intercept is the point at which the linear equation crosses the x-axis. • x-intercepts can be written as ordered pairs and may look like this: (2,0), (3,0), (-5, 0), (-8, 0) • Notice that the y-value in the ordered pair is always zero (0)

7. Finding the x-intercept • It’s important to note that the y-value is always zero because in order to find the x-intercept you will substitute zero (0) for y in a linear equation, and solve algebraically, to find the value of x. • Let’s look at an example…

8. Example #1 2x + 3y = 6 2x + 3(0) = 6 To find the x-intercept substitute zero for y and solve algebraically. 2x + 0 = 6 2 2 x = 3 The solution x=3 represents where the linear equation will cross the x-axis. The solution can be written as the ordered pair (3, 0)

9. Y-Intercepts • The y-intercept is the point at which a linear equation crosses the y-axis. • y-intercepts can be written as ordered pairs that may look like this: (0, -2), (0, 4), (0, 2), (0, -1) • Notice that in the ordered pairs the x-value is always zero (0)

10. Finding the y-Intercepts • It’s important to note that the x-value is always zero (0) because in order to find the y-intercept you substitute zero for x and solve the equation algebraically. • Let’s continue with example 1 and find the y-intercept

11. Example #1 (continued) 2x + 3y = 6 2(0) + 3y = 6 To find the y-intercept substitute zero for x and solve algebraically. 0 + 3y = 6 3 3 y = 2 The solution y=2 represents where the linear equation will cross the y-axis. The solution can be written as the ordered pair (0, 2)

12. Example #1 (continued) • Now that we have found the x and y-intercepts for the equation 2x + 3y = 6 we can plot the graph of the equation using the x and y-intercepts • To plot the graph mark the point at which the line crosses the x and y-axes and draw a line between the points • Let’s see what that looks like…

13. y x Example #1 (continued) 2x + 3y = 6 x-intercept =3 y-intercept =2 (0,2) (3,0) 2x + 3y = 6

14. Finding intercepts: • X-intercept: where the function crosses the x-axis. What is true of every point on the x-axis? • The y-value is ALWAYS zero. • Y-intercept: where the function crosses the y-axis. What is true of every point on the y-axis? • The x-value is ALWAYS zero. • Can the x-intercept and the y-intercept ever be the same point? • YES, if the function crosses through the origin!

15. Comments • Often times students get confused when working with x and y-intercepts… • They try to substitute 0 for the intercept they are looking for….this is incorrect! • If you are looking for x substitute 0 for y. • If you are looking for y substitute 0 for x

16. Practice: Find the x and y intercepts without graphing. • y – 2x = 9 (-9/2, 0) (0, 9) • 6x – 6y = 6 (1, 0) (0, -1)

17. Comments • On the next couple of slides are some practice problems…The answers are on the last slide… • Do the practice and then check your answers…If you do not get the same answer you must question what you did…go back and problem solve to find the error… • If you cannot find the error bring your work to me and I will help…

18. Your Turn • Find the x-intercept • x + 3y = 5 • 3x + 4y = 12 • -7x – 3y = 42 • Find the y-intercept • y = -2x + 5 • y = 7x – 15 • 3x + 12y = -84

19. Your Turn • Find the x and y-intercepts, graph the equation, label the points where the line crosses the axes. • y = x + 2 • y = -6 + 3x • -4x + 3y = 24 • 2x + 9y = -36

20. x = 5 x = 4 x = -6 y = 5 y = -15 y = -7 Your graph should have the following as the x and y-intercepts x = -2 y = 2 x = 2 y = -6 x = -6 y = 8 x = -18 y = -4 Your Turn Solutions

21. Summary • A key tool in making learning effective is being able to summarize what you learned in a lesson in your own words… • In this lesson we talked about Quick graphs using intercepts. Therefore, in your own words summarize this lesson…be sure to include key concepts that the lesson covered as well as any points that are still not clear to you… • I will give you credit for doing this lesson…please see the next slide…

22. Credit • I will add 10 points as an assignment grade for you working on this lesson… • To receive the full 10 points you must do the following: • Have your name, date and period as well a lesson number as a heading. • Do each of the your turn problems showing all work • Have a 1 paragraph summary of the lesson in your own words • Please be advised – I will not give any credit for work submitted: • Without a complete heading • Without showing work for the your turn problems • Without a summary in your own words…