Understanding Linear Equations

Linear equations are fundamental to Algebra and appear throughout STAAR assessments. Let's explore what makes them tick.

What is a Linear Equation?

A linear equation is an equation that, when graphed, produces a straight line. The standard forms include:

• Slope-intercept form: y = mx + b
• Point-slope form: y - y₁ = m(x - x₁)
• Standard form: Ax + By = C

Key Concepts

Slope (m)

The slope represents the rate of change — how much y changes for each unit change in x.

• Positive slope: line rises from left to right
• Negative slope: line falls from left to right
• Zero slope: horizontal line
• Undefined slope: vertical line

Y-Intercept (b)

The y-intercept is where the line crosses the y-axis (when x = 0).

TEKS Alignment

This concept aligns with several TEKS standards:

• A.2(B) — Write linear equations in various forms
• A.3(A) — Determine the slope of a line
• A.3(C) — Graph linear functions

Practice

Ready to practice? Try our linear equations practice problems.