Objective The student will be able to: complete a table for a linear equation and graph the ordered pairs. SOL: A.6, A.7bf Designed by Skip Tyler, Varina High School
List some pairs of numbers that will satisfy the equation x + y = 4. x = 1 and y = 3 x = 2 and y = 2 x = 4 and y = 0 What about negative numbers? If x = -1 then y = ? y = 5
x + y = 4 What about decimals? If x = 2.6 then y = ? Now, let’s graph the pairs of numbers we have listed.
(1, 3) (2, 2) (4, 0) (-1, 5) (2.6, 1.4) • • • • • Connect the points on your graph. What does the graph look like?
It is a straight line! It is a linear relation. • What does the line represent? • • • • All solutions for the equation x+y=4! Is (3, -1) a solution to this equation? NO! You can check by graphing it or plugging into the equation!
1) Which is a solution to 2x – y = 5? (2, 1) (3, 2) (4, 3) (5, 4) Answer Now
2) Which ordered pair is not a solution to the graph shown? (0, -1) (3, 5) (-2, -5) (-3, -1) Answer Now
3) Solve the following equation for y: 2x + y = 4 Draw “the river” Subtract 2x from both sides Simplify. Write the equation with the variable first. -2x -2x y = -2x + 4
4) Solve the following equation for y: 4x - 5y = 7 Draw “the river” Subtract 4x from both sides Simplify. Write the equation with the variable first. Divide both sides by -5 Does the fraction simplify? -4x -4x -5y = -4x + 7 -5 -5
5) Solve the following equation for y: 6x – 2y = 8 Answer Now
6) Make a table and graph the solution set of 4x + 2y = 6. Draw “the river” Subtract 4x from both sides Simplify. Write the equation with the variable first. Divide both sides by 2 Does the fraction simplify? -4x -4x 2y = -4x + 6 2 2
Let’s use the domain {0, 1, 2} for our equation. Create a t-table by picking at least three numbers to plug into our equation. Let’s use the domain {0, 1, 2} for our equation. x 1 2 ordered pair y -2(0) + 3 3 (0, 3) -2(1) + 3 1 (1, 1) -2(2) + 3 -1 (2, -1)
Draw a line through your points. It should be a straight line. Graph {(0, 3), (1, 1), (2, -1)} • • • Draw a line through your points. It should be a straight line.
Graph {(0, 3), (1, 1), (2, -1)} • • •
Which is the graph of y = -x + 3? Test using the slope slider! A B C D A B C D Answer Now
Let’s review tables! Graph y = 2x + 1 using the domain {0, 1, 4} Make sure the equation is solved for y. Create a t-table using the domain values. Plug in the domain values and solve for the range. Plot the points and connect them to create the line. x y=2x+1 y 1 4 Answer Now 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Let’s review the graphing calculator! Graph y = 2x + 1 Select TABLE from the Main Menu Make sure the equation is solved for y. Type in the right side of the equation. Select TABL (F6) from the options Type the domain values and press EXE Select G-CON from the options. This plots the points and connects them to form the line. Answer Now 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32