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Linear equations in two variables — SAT practice questions

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Practice 145 Linear equations in two variables questions in the app

What this topic is

Linear equations in two variables, such as ax + by = c, describe straight lines in the xy-plane, and questions test reading slope and intercepts from different forms.

Rewriting in slope-intercept form, y = mx + b, shows the slope as the coefficient of x. Perpendicular lines have slopes that are negative reciprocals, so a line with slope one-third is perpendicular to a line with slope negative three. Word problems ask which equation represents a situation, such as total cost when two items have different prices; each price multiplies its own variable.

Some questions ask which equation describes the same line, meaning the original multiplied through by a constant.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Mid

q x - 2 y = - 64

The given equation represents a line in the $x y$ -plane, where $q$ is a positive constant. Which equation represents the same line?

y = \frac{q}{2} x - 32

✗ Not this one

y = \frac{q}{2} x + 32

✓ Correct

y = - \frac{q}{2} x + 32

✗ Not this one

y = q x + 32

✗ Not this one

Show answer

Answer: B — $y = \frac{q}{2} x + 32$

Rewrite $q x - 2 y = - 64$ as $- 2 y = - q x - 64$ and divide by $- 2$ to get $y = \frac{q}{2} x + 32$ .

Question 2Mid

A bakery sells muffins for $3 each and cookies for $2 each. On Monday the bakery sold $m$ muffins and $c$ cookies for a total of $96. Which equation represents this situation?

3 m + 2 c = 96

✓ Correct

\frac{1}{3} m + \frac{1}{2} c = 96

✗ Not this one

3 m + 2 c = 288

✗ Not this one

m + c = 96

✗ Not this one

Show answer

Answer: A — $3 m + 2 c = 96$

Revenue from muffins is $3 m$ dollars and from cookies is $2 c$ dollars, so $3 m + 2 c = 96$ .

Question 3Easier

In the $x y$ -plane, line $m$ passes through the points $(- 1, 4)$ and $(3, - 8)$ . Which equation represents a line perpendicular to line $m$ ?

y = - \frac{1}{3} x + 2

✗ Not this one

y = \frac{1}{3} x + 2

✓ Correct

y = 3 x - 2

✗ Not this one

y = - 3 x + 2

✗ Not this one

Show answer

Answer: B — $y = \frac{1}{3} x + 2$

Line $m$ through the two points has slope $(- 8 - 4) / (3 - (- 1)) = - 3$ . A line perpendicular to $m$ has slope $1 / 3$ , which is the slope of $y = (1 / 3) x + 2$ (choice B).

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 145 Linear equations in two variables questions in the app

Linear equations in two variables — SAT practice questions

What this topic is

Sample questions

More SAT topics

Math