Algebra 1 8.2 Worksheet Answer Key

Linear Equations and Graphing

In this section, we will explore the concept of linear equations and graphing. A linear equation is an equation in which the highest power of the variable(s) is 1. Graphing is a way to visualize the relationship between variables.

8.2 Solving Linear Equations

A linear equation can be solved using addition, subtraction, multiplication, or division. The goal is to isolate the variable on one side of the equation.

Example 1: Solve for x in the equation: 2x + 5 = 11

💡 Note: To solve for x, we need to isolate x on one side of the equation.

Subtract 5 from both sides: 2x = 11 - 5 2x = 6

Divide both sides by 2: x = ⁶⁄₂ x = 3

Example 2: Solve for y in the equation: y - 3 = 7

💡 Note: To solve for y, we need to isolate y on one side of the equation.

Add 3 to both sides: y = 7 + 3 y = 10

8.2 Graphing Linear Equations

A linear equation can be graphed on a coordinate plane. The x-axis represents the independent variable, and the y-axis represents the dependent variable.

Example 3: Graph the equation: y = 2x - 3

💡 Note: To graph the equation, we need to find the x-intercept and the y-intercept.

To find the x-intercept, set y = 0: 0 = 2x - 3 2x = 3 x = ³⁄₂ x = 1.5

To find the y-intercept, set x = 0: y = 2(0) - 3 y = -3

Graph:

Answer Key:

1. 2x + 5 = 11: x = 3
2. y - 3 = 7: y = 10
3. y = 2x - 3: x-intercept = (1.5, 0), y-intercept = (0, -3)

Conclusion:

In this section, we learned how to solve linear equations using addition, subtraction, multiplication, or division. We also learned how to graph linear equations on a coordinate plane. By isolating the variable and finding the x-intercept and y-intercept, we can solve and graph linear equations.

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