Equations as Relations

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Presentation transcript:

Equations as Relations

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

Thanks for coming!