1. Problems of the Day
Express the relation {(–3, 4), (–1, 2), (–3, 3), (2, 4) (4, 3)} as a table, as a graph, and as a mapping diagram.
State the Domain of the relation.
State the Range of the relation.
State the Inverse of the relation.
{– 3, –1, 2, 4 }
{2, 3 , 4 }
{(4, –3), (2, –1), (3, –3), (4, 2) (3, 4)}

2. Equations as Relations
Algebra 1 ~ Chapter 4.4
Equations as Relations

3. Solutions to Equations
The equation y = 2x + 3 is an example of an equation in two variables (x and y)
A solution to this equation is an ordered pair (x, y), that results in a true statement when substituted into the equation.
For example, when x = 0,
y = 2(0) + 3, y = 3. So one “solution” to this equation would be x = 0 and y = 3, (0, 3)
(0, 1) would NOT be a solution because when x = 0, y ≠ 1

4. Ex. 1 - Solving Using a Replacement Set
Find the solution set for y = 2x + 3, given the replacement set {(-2, -1), (-1, 3), (0, 4), (3, 9)}
Make a table. Substitute each ordered pair into the equation. x y
y = 2x + 3
T or F? -2 -1
-1 = 2(-2) + 3
-1 = -1 T 3
3 = 2(-1) + 3
3 ≠ 1 F 4
4 = 2(0) + 3
4 ≠ 3 9
9 = 2(3) + 3
9 = 9
The ordered pairs (-2, -1) and (3, 9) result in true statements. So the solution set is {(-2, -1), (3, 9)}.

5. Ex. 2 - Solving Using a Replacement Set
Find the solution set for -3x + 2 = y, given the replacement set {(-2, 0), (-1, 5), (0, 2), (1, -1)} x y
-3x + 2 = y
T or F? -2
-3(-2) + 2 = 0
8 ≠ 0 F -1 5
-3(-1) + 2 = 5
5 = 5 T 2
-3(0) + 2 = 2
2 = 2 1
-3(1) + 2 = -1
-1 = -1
The ordered pairs (-1, 5), (0, 2) and (1, -1) result in true statements. So the solution set is {(-1, 5), (0, 2), (1, -1)}.

6. Ex. 3 - Solve Using a Given Domain
Solve y = x + 5 if the domain is {-3, -1, 0, 2, 4}.
Make a table. The values of x come from the domain. Substitute in each value of x into the equation to determine the values of y in the range. x
x + 5 y
(x, y) -3
(-3) + 5 2
(-3, 2) -1
(-1) + 5 4
(-1, 4)
(0) + 5 5
(0, 5)
(2) + 5 7
(2, 7)
(4) + 5 9
(4, 9)

7. Ex. 4 - Solve and Graph the Solution Set
Solve y = 5 – 2x if the domain is {-1, 0, 2, 4}. Graph the solution set.

8. Find the Error
Malena says that (5, 1) is a solution of y = 2x Bryan says it is not a solution. Look at their work below. Who is correct? Why?
Malena
y = 2x + 3
5 = 2(1) + 3
5 = 5
Bryan
y = 2x + 3
1 = 2(5) + 3
1 ≠ 13
Bryan is correct. Malena switched the order of the x and y-values. Bryan plugged x and y in correctly to prove (5, 1) was not a solution.

9. Assignment Study Guide 4-4 (In-Class)
Skills Practice Worksheet (Homework)