M1 Linear equations in one variable
One of the SAT's published Math skills, inside Algebra. 100 questions here, across 20 distinct question types.
Algebra on the SAT centers on linear equations, systems of equations, and inequalities, plus turning word problems into equations you can solve. Strong performance here comes from fluency with the basics: solving for a variable, working with slope and lines, and interpreting what an equation means in a real context. One concrete tip: define your variables clearly and translate each sentence of a word problem into an equation before you start solving. On this page you'll find a short lesson covering the core algebra skills with worked examples, plus free interactive practice with instant explanations so you can build speed and accuracy on the linear topics that show up most often.
Lesson
Algebra is one of the two largest domains on SAT Math — 13–15 of the 40 scored questions (about 35%), tied with Advanced Math: linear equations, systems, inequalities, and interpreting linear relationships. At the 1500+ level, the content is rarely hard — speed and accuracy are what separate scores.
What to have automatic
- Slope = (y₂ − y₁)/(x₂ − x₁); slope-intercept form y = mx + b, where b is the y-value at x = 0.
- Solutions of a linear system = the point where the lines meet. No solution = parallel (same slope, different intercept). Infinitely many = the same line.
- When you multiply or divide an inequality by a negative, flip the sign. This is the #1 careless error.
Worked examples
Solve: 5x + 3 = 2x + 18
- Get the variables on one side: subtract 2x from both sides → 3x + 3 = 18.
- Get the numbers on the other side: subtract 3 from both sides → 3x = 15.
- Divide both sides by 3 → x = 5.
- Check: 5(5) + 3 = 28 and 2(5) + 18 = 28. Both sides match, so x = 5 is correct.
A line passes through (2, 3) and (6, 11). Write its equation in slope-intercept form.
- Find the slope: m = (11 − 3) / (6 − 2) = 8/4 = 2.
- Use y = mx + b with one point. Using (2, 3): 3 = 2(2) + b.
- Solve for b: 3 = 4 + b, so b = −1.
- The equation is y = 2x − 1. Check with the other point: 2(6) − 1 = 11. ✓
Solve the inequality: 7 − 3x ≥ 22
- Subtract 7 from both sides: −3x ≥ 15.
- Divide both sides by −3. Dividing by a negative FLIPS the inequality sign.
- x ≤ −5.
- Check with x = −6: 7 − 3(−6) = 25, and 25 ≥ 22 ✓.
Common mistakes to avoid
- Forgetting to flip the inequality sign when you multiply or divide by a negative number. This is the single most common algebra error on the SAT.
- Mixing up rise and run in the slope formula. Slope is change in y over change in x, not the other way around.
- Distributing a negative incorrectly: −2(x − 5) is −2x + 10, not −2x − 10.
- Answering the wrong question. If the problem asks for 3x and you solved x = 4, the answer is 12, not 4. Always re-read what was asked.
347 questions, 137 distinct question types · you answer 12 at a time and can keep going for as long as you like.
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Frequently asked questions
What kind of algebra is on the SAT?
The algebra content focuses on linear equations and expressions, systems of two equations, and linear inequalities. You'll solve for variables, work with slope and the equation of a line, and translate word problems into equations. Many questions also ask you to interpret what a variable or coefficient means in a real-world situation. Mastering these linear fundamentals covers a large share of the math you'll see.
How do I solve systems of equations quickly?
You have two main methods: substitution, where you solve one equation for a variable and plug it into the other, and elimination, where you add or subtract equations to cancel a variable. Pick whichever fits the setup. If a variable is already isolated, substitute. If coefficients line up nicely, eliminate. Practice both so you can choose the faster path under time pressure.
How do I turn a word problem into an equation?
Start by defining what each variable stands for, including units. Then translate the words sentence by sentence: is means equals, per signals a rate, and total or sum points to addition. Write one equation for each relationship the problem describes. Once your equations capture the situation, solving is the easy part. Rushing this translation step is where most word-problem mistakes happen.
What does slope mean in a word problem?
Slope is the rate of change: how much the output changes for each one-unit increase in the input. In context, it's often a per-unit amount, like dollars per hour or miles per gallon. The y-intercept is the starting value when the input is zero. When a question asks what a number in an equation represents, connect slope to a rate and the intercept to a starting point.