Linear Equations

A linear equation is an equation that represents a straight line when graphed on a coordinate plane. The general form of a linear equation in one variable is: y = mx + b, where y represents the dependent variable, x represents the independent variable, m is the slope, and b is the y-intercept.

Slope-Intercept Form

The slope-intercept form of a linear equation is y = mx + b. The slope (m) represents the rate of change of the line, and the y-intercept (b) represents the point where the line intersects the y-axis.

Point-Slope Form

The point-slope form of a linear equation is y - y₁ = m(x - x₁). This form is useful when you know the slope and a point on the line.

Standard Form

The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. This form is useful for graphing and finding the x and y-intercepts.

Graphing Linear Equations

To graph a linear equation, you can use the slope-intercept form to identify the y-intercept and slope, or you can use the x and y-intercepts if the equation is in standard form.

Solving Linear Equations

To solve a linear equation, you can use various methods such as substitution, elimination, or graphing. The goal is to isolate the variable (x or y) to find its value.

Study Guide

• Understand the different forms of linear equations: slope-intercept form, point-slope form, and standard form.
• Be able to identify the slope and y-intercept from the equation in slope-intercept form.
• Practice graphing linear equations and finding the x and y-intercepts.
• Practice solving linear equations using various methods.
• Understand the relationship between the equation of a line and its graphical representation.

Remember to always check your solutions by substituting the values back into the original equation to ensure they satisfy the equation.

[Linear Equations] Related Worksheets and Study Guides:

• Solving linear equationsMathematics • Eighth Grade