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Linear equations in two variables — SAT practice questions

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Practice 143 Linear equations in two variables questions in the app

What this topic is

Linear equations in two variables on the SAT Math section covers writing, rewriting, and interpreting a line in the xy-plane, including slope and equivalent forms of the same relationship.

Sample questions

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

Question 1Mid

$qx-2y=-64$

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

A$y=\dfrac{q}{2}x-32$✗ Not this oneB$y=\dfrac{q}{2}x+32$✓ CorrectC$y=-\dfrac{q}{2}x+32$✗ Not this oneD$y=qx+32$✗ Not this one

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Answer: B — $y=\dfrac{q}{2}x+32$

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

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?

A$3m + 2c = 96$✓ CorrectB$\dfrac{1}{3}m + \dfrac{1}{2}c = 96$✗ Not this oneC$3m + 2c = 288$✗ Not this oneD$m + c = 96$✗ Not this one

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Answer: A — $3m + 2c = 96$

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

Question 3Easier

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

A$y=-\dfrac{1}{3}x+2$✗ Not this oneB$y=\dfrac{1}{3}x+2$✓ CorrectC$y=3x-2$✗ Not this oneD$y=-3x+2$✗ Not this one

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Answer: B — $y=\dfrac{1}{3}x+2$

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).

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