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Linear equations in two variables — SAT practice questions

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. A student has to produce an equation from two points, identify a line perpendicular to a given line, rewrite an equation that still describes that graph, and model a word problem such as bakery sales as an equation in two unknowns. Questions are usually multiple choice, with similar-looking linear equations as options. Common traps include keeping the original slope instead of the negative reciprocal, slips when isolating y, and pairing the wrong variable with the wrong unit price.

  • Section: Math 44 questions on the paper
  • 143 practice questions in the app

Sample questions

Question 1

qx−2y=−64qx-2y=-64

The given equation represents a line in the xyxy-plane, where qq is a positive constant. Which equation represents the same line?

  1. Ay=q2x−32y=\dfrac{q}{2}x-32
  2. By=q2x+32y=\dfrac{q}{2}x+32
  3. Cy=−q2x+32y=-\dfrac{q}{2}x+32
  4. Dy=qx+32y=qx+32
Show answer

Answer: B — y=q2x+32y=\dfrac{q}{2}x+32

Rewrite qx−2y=−64qx-2y=-64 as −2y=−qx−64-2y=-qx-64 and divide by -2 to get y=q2x+32y=\dfrac{q}{2}x+32.

Question 2

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

  1. A3m+2c=963m + 2c = 96
  2. B13m+12c=96\dfrac{1}{3}m + \dfrac{1}{2}c = 96
  3. C3m+2c=2883m + 2c = 288
  4. Dm+c=96m + c = 96
Show answer

Answer: A — 3m+2c=963m + 2c = 96

Revenue from muffins is 3m3m dollars and from cookies is 2c2c dollars, so 3m+2c=963m + 2c = 96.

Question 3

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

  1. Ay=−13x+2y=-\dfrac{1}{3}x+2
  2. By=13x+2y=\dfrac{1}{3}x+2
  3. Cy=3x−2y=3x-2
  4. Dy=−3x+2y=-3x+2
Show answer

Answer: B — y=13x+2y=\dfrac{1}{3}x+2

Line mm through the two points has slope (−8−4)/(3−(−1))=−3(-8-4)/(3-(-1))=-3. A line perpendicular to mm has slope 1/31/3, which is the slope of y=(1/3)x+2y=(1/3)x+2 (choice B).

Practice 143 Linear equations in two variables questions in the app

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