1. 4-4 Equations as Relations
Objectives
1. use an equation to determine the range
for a given domain
2. graph the solution set for a given
domain

2. The equation p = 0.69d is an example of an equation in two variables.
A solution of an equation in two variables is an ordered pair that results in a true statement when substituted into the equation.

3. 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

4. x + y = 4 What about decimals? If x = 2.6 then y = ?
Now, let’s graph the pairs of numbers we have listed.

5. (1, 3) (2, 2) (4, 0) (-1, 5) (2.6, 1.4) • • • • •
Connect the points on your graph.
What does the graph look like?

6. 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!

7. 1) Which is a solution to 2x – y = 5?
(2, 1)
(3, 2)
(4, 3)
(5, 4)
Answer Now

8. 2) Which ordered pair is not a solution to the graph shown?
(0, -1)
(3, 5)
(-2, -5)
(-3, -1)
Answer Now

9. 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 x
y = -2x + 4

10. 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 x
-5y = -4x + 7

11. 5) Solve the following equation for y: 6x – 2y = 8
Answer Now

12. 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 x
2y = -4x + 6

13. Let’s use the domain {0, 1, 2} for our equation.
Create a t-chart 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) (0, 3)
-2(1) (1, 1)
-2(2) (2, -1)

14. 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.

15. Graph {(0, 3), (1, 1), (2, -1)} • • •

16. Which is the graph of y = -x + 3?B A D C A B C D
Answer Now