Question 1Easier
What is the value of in the equation ?
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Answer: C — 7
Divide both sides by 5 to get . Adding 3 to both sides gives .
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Mathematics
Linear equations and slope — SHSAT practice questions
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What this topic is
Slope measures how steep a line is, the change in y divided by the change in x, and it is the thread running through this topic.
Parallel lines share a slope, while perpendicular lines have slopes that are negative reciprocals, so a line with slope two-thirds is perpendicular to one with slope negative three-halves. Linear equations and slope questions also ask for the solution of an equation, often after distributing a number across parentheses.
Word problems describe a fixed fee plus a cost per person, which is a linear model; setting up the equation correctly is usually harder than solving it. Checking the answer in the original equation catches slips.
Sample questions
Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.
Question 2Mid
A club pays a fixed 240 dollar rental fee plus 12 dollars per student for a trip. If the total cost is divided equally among all students, how many students must go for the cost per student to be 18 dollars?
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Answer: C — 40
For students, the total cost is . Since each student pays $18, , so and .
Question 3Mid
Which line is perpendicular to ?
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Answer: A —
Perpendicular slopes are negative reciprocals, so the slope must be .
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Practice 229 Linear equations and slope questions in the app
More SHSAT topics
Mathematics
- Number system and operations
- Ratios, unit rates, and proportional relationships
- Percentages (incl. percent change)
- Exponents and scientific notation
- Algebraic expressions
- Inequalities
- Systems of equations
- Functions
- Angles and lines
- Triangles and the Pythagorean theorem
- Area, perimeter, volume, and surface area
- Coordinate plane and distance
- Scale drawings and transformations
- Statistics (center, spread, plots)
- Probability and counting
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