Graphing Linear Equations on the SAT

Why the SAT Emphasizes Graphing Linear Equations

A line on a graph tells a story about a relationship. The SAT often gives you an equation and asks which graph matches, or it gives you a graph and asks for the equation that created it. If you can find the intercept and the slope, you can answer these questions quickly.

This lesson shows two fast entry points, slope intercept form and intercepts. You will also see how to rewrite standard form without losing a sign, and how to avoid mixing up the $x$ intercept with the $y$ intercept.

A Simple Definition Unlocks Graphing Linear Equations

In $y = mx + b$, the slope $m$ tells you how steep the line is and the intercept $b$ tells you where it crosses the $y$ axis. If you know those two values, you can sketch the line in seconds.

When an equation is in standard form, like $2x + 3y = 6$, solve for $y$ so you can read $m$ and $b$. Be careful, the sign of $b$ is easy to misread when you divide through.

Work Through Graphing Linear Equations Step by Step

Convert the equation to slope intercept form so you can see the slope and intercept, then plot those points carefully.

Use Desmos to Check Graphing Linear Equations

Desmos graphs instantly, which is great when the equation is messy or when you want to confirm an intercept. It is also helpful when an answer choice is a graph.

Algebra is faster for spotting the slope and intercept in your head. Desmos is faster when you need to compare multiple graphs or avoid a sign mistake.

Expert move: Graph the lines and use intersections for "when do they match?" questions; Desmos also verifies slope and intercepts quickly when coefficients are messy.

When to skip Desmos: For quick slope or parallel/perpendicular checks, algebra is faster; use Desmos for verification.

• Desmos features used: graphing, intercepts.
• Common mistake: reading the $x$ intercept as the $y$ intercept.

Practice Graphing Linear Equations with SAT-Style Questions

Focus on intercepts and slope in each question.

Key Takeaways to Remember for Graphing Linear Equations

• Convert to $y = mx + b$ to read slope and intercept quickly.
• Intercepts are found by setting the other variable to $0$.
• Desmos is excellent for checking graphs and intercepts quickly.