Warm Ups

{(2,0) (-1,3) (2,4)}

1. Write as table

2. Write as graph

3. Write as map

4. State domain & range

5. State the inverse

5-3 Equations as Relations

Objective: To determine solutions to equations.

Standard 16.0

Ordered pairs: always write in alphabetical order

(x, y) (a, b) (r, s)

Linear Equation: an equation that, when graphed, creates a straight line.

Solution: ordered pairs that give a true statement

Example 1Which of these are solutions of 3x + y = 8 ?1. Plug in the values for x and y

2. Simplify each side

3. Check if they are equal

(4,-4) (8,0) (2,2) (3,1) x y

3(4) + (-4) = 8

12 + -4 = 8

8 = 8

Yes!

x y

3(8) + 0 = 8

24 + 0 = 8

24 = 8

No!

x y

3(2) + 2 = 8

6 + 2 = 8

8 = 8

Yes!

x y

3(3) + 1 = 8

9 + 1 = 8

10 = 8

No!

Example 2

Solve the equation 2x + 2y = 14 given x = -31. Substitute

2. Solve for remaining variable

3. Write as ordered pair

2x + 2y = 14

2(-3) + 2y = 14

-6 + 2y = 14

+6 +6

2y = 20

y = 10(-3, 10)

Given the domain…

Solve the equation x + y = 4 if the domain is {-4, -2, 0, 2, 4}Plug it in, domain = x

Answer as ordered pairs!

What if…

I gave you the range instead of the domain?

How would you solve the equation given the range? Plug the values in for y, then solve for x

Example 3

Make a table and graph y = x + 6 if the domain is {-4,-3,2,4}

Answer:

(-4,2) (-3,3) (2,8) (4,10)

This is a linear equation so you should be able to

connect the dots and make a line.

TOO

1. y = -1 for 3x = 13 – 2y

2. x = 10 for 5x + 3 = y

Answers

1. (5, -1)

2. (10, 53)

Homework

5-3 Practice