Test yourself on Linear Equations with 10 original SAT practice questions. Pick an answer to see instant feedback and a full explanation.
Free original practice questions for study purposes. Open Exam Prep is an independent study resource and is not affiliated with, endorsed by, or sponsored by the makers of SAT.
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Answer the questions below — you get instant feedback and a full explanation for each.
1. If 3x + 7 = 22, what is the value of x?
Explanation. Subtract 7 from both sides: 3x = 15. Divide by 3: x = 5.
2. A line passes through the points (2, 3) and (6, 11). What is its slope?
Explanation. Slope = (11 − 3)/(6 − 2) = 8/4 = 2.
3. The equation of a line is y = -3x + 5. What is the y-intercept?
Explanation. In slope-intercept form y = mx + b, the y-intercept is b = 5.
5. A line has equation 4x + 2y = 12. What is the slope of a line perpendicular to it?
Explanation. Solve for y: 2y = −4x + 12, so y = −2x + 6, slope = −2. The perpendicular slope is the negative reciprocal: 1/2.
6. For what value of c does the equation 6x + 4 = 2(3x + c) have infinitely many solutions?
Explanation. Expand the right side: 2(3x + c) = 6x + 2c. For infinitely many solutions both sides must be identical: 4 = 2c, so c = 2.
7. A taxi charges a flat fee of $3 plus $0.50 per mile. Which equation gives total cost C for m miles?
Explanation. The flat fee $3 is the constant, and $0.50 per mile is the rate: C = 3 + 0.50m.
8. If the line y = mx + 4 passes through the point (3, 16), what is m?
Explanation. Substitute: 16 = m(3) + 4. So 12 = 3m, giving m = 4.
9. The system 2x + y = 7 and x − y = 2 has what solution (x, y)?
Explanation. Add the equations: 3x = 9, so x = 3. Then y = x − 2 = 1. Solution is (3, 1).
10. For what value of k does the system kx + 2y = 6 and 3x + y = 4 have NO solution?
Explanation. No solution means parallel lines: equal slopes, different intercepts. Slope of second line is −3 (from y = −3x + 4). First line slope = −k/2. Set −k/2 = −3, so k = 6. Check intercepts differ: first gives y = 3 at x=0, second gives 4, so they are parallel and distinct.
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FAQ
What forms of linear equations do I need to know for the SAT?
Master slope-intercept form (y = mx + b), standard form (Ax + By = C), and point-slope form. Be comfortable converting between them and identifying slope and intercepts quickly.
How do I handle 'no solution' or 'infinitely many solutions' problems?
Compare the lines. Infinitely many solutions means the two equations are multiples of each other (same slope AND same intercept). No solution means parallel lines (same slope but different intercept). Identifying slopes is usually the fastest first step.
What's the most common mistake on linear equation questions?
Sign and distribution errors. When you distribute a negative or move terms across the equals sign, carefully track signs. Also remember perpendicular slopes are negative reciprocals, not just negatives.