4.4 Equations as Relations

• 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.

Solve 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.

• The ordered pairs (-2 , -1) and (3 , 9) result in true statements. The solution set is {(-2 , -1) , (3 , 9)}.

Solve Using a Given Domain• Solve b = a + 5 if the domain is {-3 , -1, 0 , 2 , 4}.• Make a table. The values of a come from the domain.

Substitute each value of a into the equation to determine the values of b in the range.

• The solution set is {(-3 , 2) , (-1 , 4) , (0 , 5), (2 , 7) , (4 , 9)}

Graph Solution Sets

• You can graph the ordered pairs in the solution set for an equation in two variables.

• The domain contains values represented by the independent variable.

• The range contains the corresponding value represented by the dependent variable.

Solve and Graph the Solution Set• Solve 4x + 2y = 10 if the domain is {-1 , 0 , 2 ,

4}. Graph the solution set.

• First solve the equation for y in terms of x. This makes creating a table of values easier.

4 2 10x y 4 2 4 10 4x y x x 2 10 4y x 2 10 4

2 2

y x 5 2y x

Solve and Graph the Solution Set• Substitute each value of x from the domain to

determine the corresponding values of y in the range. Then, graph the solution set.

Solve for a Dependent Variable

• See example 4 on p. 213.