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# 7 1solve By Graphing

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### 7 1solve By Graphing

1. 1. Solving Linear Equations Using Graphing Substitution and Elimination Introduction to Unit Six
2. 2. What’s the Deal? <ul><li>There are a number of ways to solve groups of linear equations. </li></ul><ul><li>In this lesson, we will find points on a coordinate plane that solve linear equations in standard form and y-intercept form. </li></ul>
3. 3. Three Parts (over the next few days) <ul><li>Part One – Solve linear equations by graphing. </li></ul><ul><li>Part Two – Solve linear equations by substitution. </li></ul><ul><li>Part Three – Solve linear equations by elimination. </li></ul>
4. 4. Solving for linear equations answers the question: <ul><li>What values of x and y fit into both equations? </li></ul><ul><li>The answer is usually given in (x,y) format (ie. (-4, 6) or (3,8). </li></ul>
5. 5. Remember - Slope intercept form: y = mx + b <ul><li>m = slope </li></ul><ul><li>b = y-intercept </li></ul><ul><li>In y = 1/2x – 7 , </li></ul><ul><ul><li>What is the y-intercept? </li></ul></ul><ul><ul><li>What is the slope? </li></ul></ul><ul><li>Rise over Run </li></ul><ul><ul><li>Rise = up, or plus one (+1) </li></ul></ul><ul><ul><li>Run = right, or plus two (+2). </li></ul></ul>
6. 6. If the slope is ½ <ul><li>Rise </li></ul><ul><li>Run = slope = m </li></ul><ul><li>The rise is 1 and the run is 2. </li></ul><ul><li>From the origin (0,0), go up 1 and right 2. </li></ul>
7. 7. Graphing Systems of equations <ul><li>y = 3x + 1 </li></ul><ul><li>y = -x + 5 </li></ul><ul><li>Since both are in y-intercept format (y=mx+b) find the point through which the line intercepts the y-axis. </li></ul><ul><li>Graph these equations. Answers on the next slides. </li></ul>
8. 8. Graph on the board Graph y = 3x + 1 y = -x + 5
9. 9. Graphs y = 3x + 1 y = -x + 5
10. 10. Solving By Graphing Which point or points can fit into both equations? The result is the ( x,y ) coordinates of the intersection.
11. 11. The coordinates of the intersecting point is your solution. The lines inter- cept at (1, 4) so the solution is x=1, y =4. The lines inter- cept at (1, 4) so the solution is x=1, y =4.
12. 12. Solve by graphing <ul><li>y = x +3 </li></ul><ul><li>y = x +1 </li></ul><ul><li>The next two slides will show the solution. </li></ul>
13. 13. The coordinates of the intersecting point is your solution. The lines inter- cept at (-20,-12) so the solution is x= -20, y = -12.
14. 14. Now solve equations in standard form. <ul><li>3 x + 2y = -6 and </li></ul><ul><li>-3 x + 2y = 6 </li></ul><ul><li>Step One: Convert equations from standard form to y-intercept form. </li></ul><ul><li>Let’s review that from a previous lesson using the equations above… </li></ul>
15. 15. Change 3x + 2y = -6 to y-intercept form <ul><li>3x + 2y = -6 </li></ul><ul><li>- 3x -3x </li></ul><ul><li>-2y = -3x - 6 </li></ul><ul><li>Now we need to get y isolated. In this case, let’s divide both sides by 2. </li></ul><ul><li>2y = -3x - 6 </li></ul><ul><li>2 2 2 </li></ul><ul><li>Now simplify. y = - x -3 </li></ul>Subtract -3x from both sides
16. 16. Change -3x + 2y = 6 to y-intercept form <ul><li>-3x + 2y = +6 </li></ul><ul><li>+ 3x 3x </li></ul><ul><li>2y = 3x + 6 </li></ul><ul><li>Get y isolated. Divide both sides by 2. </li></ul><ul><li>2y = 3x + 6 </li></ul><ul><li>2 2 2 </li></ul><ul><li>Now simplify. y = 3 / 2 x + 3 </li></ul>Add 3x to both sides
17. 17. Graph the equations: y = - 3 / 2 x -3 and y = 3 / 2 x + 3 x = 2, y = 0 The solution is (2,0)
18. 18. Math is NOT a Spectator Sport Write it Out!
19. 19. End of Part One Assignment: pg. 323-4: 10 - 27
20. 20. Extras for presentation x y -4 -2 0 +2 +4 -6 -4 -2 0 +2 +4 +6