1. Holt Algebra 2 3-Ext Parametric Equations Graph parametric equations, and use them to model real-world applications. Quiz Review

2. Holt Algebra 2 3-Ext Parametric Equations Check It Out! Example 1a Write equations for and draw a graph of the motion of the helicopter. A helicopter takes off with a horizontal speed of 5 ft/s and a vertical speed of 20 ft/s. Using the horizontal and vertical speeds given above, write equations for the ground distance x and altitude y in terms of t. Use the distance formula d = rt. x = 5t y = 20t

3. Holt Algebra 2 3-Ext Parametric Equations Make a table of values to help you draw the graph. Use different t-values to find x- and y-values. The x and y rows give the points to plot. Check It Out! Example 1a Continued t02468 x010203040 y0 80120160    

4. Holt Algebra 2 3-Ext Parametric Equations Check It Out! Example 2 Write an equation for the helicopter's motion in terms of only x and y. Recall that the helicopter in Check It Out Problem 1 takes off with a horizontal speed of 5 ft/s and a vertical speed of 20 ft/s. y = 4x y = 20t Solve for t in the first equation. Second equation Substitute and simply. x = 5t, so y = 20 = 4x The equation for the airplane’s altitude in terms of ground distance is y = 4x.

5. Holt Algebra 2 3-Ext Parametric Equations Guided Practice: Express y in terms of x 1)x =20t y= 100t 2)x=4t y= 9t 3)x=8t y= 80t 4)x=4t y= 2t 5)x=9t y= 36t

6. Holt Algebra 2 3-Ext Parametric Equations Use substitution to determine if the given ordered pair is an element of the solution set for the system of equations. Example 1A: Verifying Solutions of Linear Systems (1, 3); x – 3y = –8 3x + 2y = 9 Substitute 1 for x and 3 for y in each equation. Because the point is a solution for both equations, it is a solution of the system. 3x + 2y = 9 3(1) +2(3) 9 9 9 x – 3y = –8 (1) –3(3) –8–8 –8–8–8–8

7. Holt Algebra 2 3-Ext Parametric Equations Check It Out! Example 1a Use substitution to determine if the given ordered pair is an element of the solution set for the system of equations. (4, 3); x + 2y = 10 3x – y = 9 Because the point is a solution for both equations, it is a solution of the system Substitute 4 for x and 3 for y in each equation. x + 2y = 10 (4) + 2(3) 10 9 3(4) – (3) 3x – y = 9 9 9

8. Holt Algebra 2 3-Ext Parametric Equations Use a graph and a table to solve the system. Check your answer. Example 2A: Solving Linear Systems by Using Graphs and Tables 2x – 3y = 3 y + 2 = x Solve each equation for y. y= x – 2 y= x – 1 On the graph, the lines appear to intersect at the ordered pair (3, 1)