Linear equations and slope — SHSAT practice questions

Linear equations and slope on the SHSAT Mathematics test covers one-variable equations, the slope of a line, and how slopes of parallel and perpendicular lines relate. A student has to distribute and isolate a variable, decide which listed line is perpendicular to a given line, and write a linear model from a story that combines a fixed fee with a per-student charge so a target cost per person can be met. Questions are multiple choice, with numbers or line equations as options. Traps include dropping the negative on a perpendicular slope, mixing parallel with perpendicular, and dividing only the variable cost instead of the full total.

Section: Mathematics 57 questions on the paper
218 practice questions in the app

Sample questions

Question 1

What is the value of $x$ in the equation $5(x-3)=20$ ?

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Answer: C — 7

Divide both sides by 5 to get $x-3=4$ . Adding 3 to both sides gives $x=7$ .

Question 2

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 $s$ students, the total cost is $240+12s$ . Since each student pays 18, $\dfrac{240+12s}{s}=18$ , so $240+12s=18s$ and $s=40$ .

Question 3

Which line is perpendicular to $y=\tfrac{2}{3}x+1$ ?

A $y=-\tfrac{3}{2}x+4$
B $y=\tfrac{3}{2}x+4$
C $y=-\tfrac{2}{3}x+4$
D $y=\tfrac{2}{3}x-1$

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Answer: A — $y=-\tfrac{3}{2}x+4$

Perpendicular slopes are negative reciprocals, so the slope must be $-\tfrac{3}{2}$ .

Practice 218 Linear equations and slope questions in the app

Linear equations and slope — SHSAT practice questions

Sample questions

More SHSAT topics

Mathematics