Review Graphing Linear Equations

1. ReviewGraphing Linear Equations A review of sections 4.2, 4.3, and 4.5 Mike Hagedorn CEP 811 STaIR

2. Standards and Objectives • Objectives • The learner will review the three different methods of graphing linear equations. • The learner will be given specific equations and/or story problems and will be forced to decide with method is the most efficient • Standards • A3.1.1 Write the symbolic forms of linear functions (standard, point-slope, and slope-intercept) given appropriate information, and convert between forms. • A3.1.2 Graph lines (including those of the form x = h and y = k) given appropriate information. • A3.1.3 Relate the coefficients in a linear function to the slope and x- and y-intercepts of its graph.

3. Introduction • This project is designed to allow students to review graphing linear equations on their own. Use this project as a way to prepare yourself for the test. Take your time and make sure you are fully comfortable with the content. There will be links throughout this project that will take you to various web pages and help clarify any misunderstandings. DIRECTIONS Go through each this project by clicking the arrows Go through and review each method. If you need to review something, you may click the back button. Once you have completed the review, complete the practice quiz and attempt to answer them correctly If you feel you need to review some more, click the homebutton. There will also be various links throughout to help youwhich will be underlined in red for you to click on if needed Move on to the next section

4. Vocabulary to know • Ordered pair • Linear equation • X-intercept • Y-intercept • Slope • Slope intercept form

5. Graph linear equations using tables • Start with equation in two variables • Example: • A solution is the ordered pair that produces a true statement • Need several to be able to create a graph • Let’s graph • First: make a table by choosing a few values for x • Second: substitute each x into the equation and find the value of y • Plot the corresponding points on a graph • Connect the points

6. Let’s practice • Graph the following equation using a table • Let’s use for our x values in our table to find the corresponding y values • The table as follows • 2. Now let’s plot the points and connect the dots

7. Graph linear equations using intercepts • Intercepts: the two points where the graph of the line crosses the axes • x-intercept: where the graph crosses the x-axis. Will have the ordered pair • y-intercept: where the graph crosses the y-axis. Will have the ordered pair To find each intercept To find x-intercept: To find y-intercept: Let y = 0, Let x = 0, then solve for x then solve for y Once you have the two intercepts, plot them on a graph and connect the dots! There’s the graph for that equation.

8. Example Solving and graphing interepts • Find the intercepts of • x-int: Let y = 0 • y-int: Let x = 0 • So our is 7, and our is 2 • Now lets graph this!

9. Let’s practice • Graph the following linear equation by finding the intercepts • Find the x-intercept (let y = 0) • Find the y-intercept (let x = 0) • Now plot the points (intercepts) on the graph

10. Graph linear equations using slope-intercept form • Easiest way to graph!!!!!! • The equation is: • Need to know the slope. • Can do this by counting the grid lines on a graph if graph is already there, OR • Using the equation if two points are known that lie on the line. • Will commonly be the coefficient or in other words, the number next to the x in most problems. • The other thing you need is the y-intercept • Is the constant term in the equation. Example Slope y-intecept

11. To graph using Slope-intercept form • First: • Get the equation into slope-intercept form (y by itself) • Second: • Plot the y-intercept on the graph Third • From the y-intercept, apply the slope to get a second point, then connect the dots Example: Graph ; follow the three steps 1. Already in slope-intercept form 2. Plot the y-intercept: b = 2 3. From y-intercept, apply slope Rise Run

12. Let’s practice • Graph the following equation using slope-intercept form • Get equation into slope-intercept form (get y by itself) • 2. Plot y-intercept • 3. Apply the slope from the y-intercept to get a second point y-intercept slope

13. Practice Quiz!!!!!! • Choose the correct letter for each question • Be sure took look closely at all information before selecting a choice • Take your time. Use pencil and paper if you need to

14. Problem #1 • Which table matches the following graph • a) • b) • c) • d)

15. Problem #2 a) x-intercept: 10 (10, 0) • y-intercept: -16 (0, -16) • b) x-intercept: -10 (-10, 0) • y-intercept: 16 (0, 16) • c) x-intercept: 8 (8, 0) • y-intercept: -5 (0, -5) • d) x-intercept: -8 (-8, 0) • y-intercept: 5 (0, 5) • What is the x-intercept and y-intercept of the following equation?

16. Problem #3 • Which graph matches the following x and y intercepts c) a) b) d)

17. Problem #4 • The slope and y-intercept of the following graph are? • Slope (m): 4 • y-intercept (b): -7 • Slope (m): -4 • y-intercept (b): -7 • Slope (m): 4 • y-intercept (b): 7 • Slope (m): -4 • y-intercept (b): 7

18. Problem #5 • Which graph matches the following linear equation? a) c) b) d)

19. Try Again… • Be sure to check your math and watch your signs.

20. Try Again… • Put in zero for one variable, then solve for the other Here is a video to help solve for the x and y intercept

21. Try Again… • Look closely at the signs of the values and match them on the graph

22. Try Again… • Try counting the grid lines to help.

23. Try Again… • Remember our steps to graph using slope-intercept form • Start with ?????, then apply????

24. Great Job!!!!

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28. Great Job!!!! Push for the next problem

29. Congratulations!!!! • You completed the tutorial and now are ready for the test. Push esc button