Page 127 - Algebra 1

A solution to an equation with two variables is an ordered pair that makes the equation true. There are infinite solutions to the equation y = 4x + 2. Solutions can be found by substituting values for the independent variable, x, to find the corresponding value of the dependent variable, y.
Determining the Dependent Variable
Complete the table for the equation y = 4x + 2.
SOLUTION
Substitute the x-values into the equation to determine the y-values. First substitute -2 for x in the equation.
Example
3
x
y
-2
0
2
_3 4
Caution
Be sure to use the order of operations when simplifying either side of an equation.
y = 4x + 2
y = 4(-2) + 2
y = -8 + 2
y = -6
One solution to the equation is the ordered pair (-2, -6). Then substitute the other values to complete the table.
Write the equation. Substitute -2 for x. Evaluate.
Math Reasoning
Generalize How are the independent and dependent variables graphed on the coordinate plane?
x = 0
y = 4x + 2
y = 4(0) + 2 y = 0 + 2
y = 2
x = 2
y = 4x + 2
y = 4(2) + 2 y = 8 + 2
y = 10
x = _3 4
The completed table shows the ordered pairs for the given values of x.
y = 4x + 2 _3
y = 4(4)+ 2 y = 5
x
y
-2
-6
0
2
2
10
_3 4
5
112 Saxon Algebra 1
Values are assigned to the variable x. The value of the variable y is dependent on the value chosen for the variable x.