3 Ext Parametric Equations Quiz Review Graph parametric

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

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

3 -Ext Parametric Equations Check It Out! Example 1 a Continued 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. t 0 2 4 6 8 x 0 10 20 30 40 y 0 40 80 120 160 Holt Algebra 2

3 -Ext Parametric Equations Check It Out! Example 2 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. Write an equation for the helicopter's motion in terms of only x and y. x = 5 t, so Solve for t in the first equation. y = 20 t y = 20 Second equation = 4 x Substitute and simply. y = 4 x The equation for the airplane’s altitude in terms of ground distance is y = 4 x. Holt Algebra 2

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

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

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

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