20 easy SAT Linear equations · two variables questions
These are the questions most test-takers get right. They are worth practising anyway: on the digital SAT the easy questions in Module 1 are what route you into the harder, higher-scoring Module 2, so dropping one costs more than it looks.
Every question below is a real item from the SAT Climb bank, tagged easy by the same difficulty model the app uses to build your practice. Pick an answer before you open the explanation.
In the xy-plane, the graph of the equation 6x+2y=24 is parallel to the graph of which of the following equations?
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Why A is right
Parallel lines have the same slope. Rewriting 6x+2y=24 in slope-intercept form gives y=−3x+12, so the slope is -3. Choice A, 3x+y=10, can be rewritten as y=−3x+10, which also has slope -3.
Why the others are wrong
BThis equation has slope -1/3, not -3, resulting from swapping the coefficients.
CThis equation has slope 3, not -3, due to the opposite sign.
DThis equation has slope -1/3, not -3, from reversing the coefficient ratio.
Question 2Easy
The temperature of a cooling object is modeled by the equation T=200−8t, where T is the temperature in degrees Fahrenheit and t is the time in minutes since cooling began. Which statement is the best interpretation of 8 in this context?
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Why D is right
In the equation T=200−8t, the coefficient -8 is multiplied by t (time in minutes). The negative sign indicates the temperature decreases, and the magnitude 8 means it decreases by 8 degrees Fahrenheit for each minute that passes.
Why the others are wrong
AThis uses the wrong operation; since the coefficient is -8 (negative), the temperature decreases rather than increases.
BThis interprets 8 as the initial temperature, but the constant term 200 represents the initial temperature of the object.
CThis represents an arithmetic slip, misreading 8 as 0.8 by incorrectly placing a decimal point.
Question 3Easy
In the xy-plane, the graph of the equation 4x−3y=12 has an x-intercept of (a, 0). What is the value of a?
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Why B is right
The x-intercept occurs when y=0. Substituting y=0 into the equation gives 4x−3(0) = 12, which simplifies to 4x=12, so x=3. Therefore a=3.
Why the others are wrong
AThis results from an incorrect sign operation when solving for x.
CThis is the coefficient of x in the equation, not the x-intercept.
DThis is the constant term without dividing by the coefficient of x.
Question 4Easy
A company produces x units of Product A and y units of Product B. Each unit of Product A requires 2 hours of assembly time, and each unit of Product B requires 7 hours of assembly time. The total assembly time for both products is 140 hours. Which equation represents this situation?
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Why A is right
Since each unit of Product A requires 2 hours and x units are produced, the total time for Product A is 2x hours. Since each unit of Product B requires 7 hours and y units are produced, the total time for Product B is 7y hours. The equation 2x+7y=140 represents the total assembly time.
Why the others are wrong
BThis incorrectly swaps the coefficients, assigning 7 hours to Product A and 2 hours to Product B.
CThis incorrectly uses subtraction instead of addition for combining the assembly times.
DThis omits the different time requirements for each product, treating both as requiring 1 hour.
Question 5Easy
In the xy-plane, line l passes through the origin and the point (3, 12).
Which equation defines line l?
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Why B is right
The line passes through the origin (0, 0) and (3, 12). The slope is (12 - 0)/(3 - 0) = 12/3 = 4. Since the line passes through the origin, the y-intercept is 0, so the equation is y=4x.
Why the others are wrong
AThis results from incorrectly dividing 12 by 4 instead of 3 by 12, reversing the numerator and denominator in the slope calculation.
CThis incorrectly uses the y-coordinate of the given point as the y-intercept instead of recognizing the line passes through the origin.
DThis results from using the y-coordinate as the slope instead of computing rise over run.
Question 6Easy
In the xy-plane, the graph of the equation 9x+3y=27 is parallel to the graph of which equation?
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Why B is right
Rewriting 9x+3y=27 in slope-intercept form gives 3y=−9x+27, or y=−3x+9. Parallel lines have the same slope, so the answer must have slope -3.
Why the others are wrong
AThis has the opposite sign for the slope.
CThis uses the coefficient of x from the original equation instead of the calculated slope.
DThis incorrectly inverts the slope value.
Question 7Easy
A phone plan charges customers according to the equation T=0.08n+30, where T is the total monthly cost in dollars and n is the number of text messages sent. Which statement is the best interpretation of 30 in this context?
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Why D is right
In the equation T=0.08n+30, the constant 30 is added regardless of the number of text messages sent. This represents a fixed charge that does not depend on n, so the plan charges $30 as a fixed monthly fee.
Why the others are wrong
AThis interprets 30 as the per-message rate, but 0.08 is the coefficient of n and represents the charge per text message.
BThis represents an arithmetic error, misreading 30 as 0.30 by incorrectly placing a decimal point.
CThis uses the wrong operation; since 30 is added (positive), it increases the total cost rather than decreasing it.
Question 8Easy
In the xy-plane, the graph of the equation 4x−3y=12 intersects the x-axis at the point (a, 0). What is the value of a?
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Why C is right
At the x-intercept, y=0. Substituting y=0 into 4x−3y=12 gives 4x=12, so x=3. Therefore a=3.
Why the others are wrong
AThis incorrectly applies a negative sign to the result.
BThis confuses the coefficient of y with the x-intercept value.
DThis is the coefficient of x, not the x-intercept value.
Question 9Easy
A factory produces small bolts and large bolts. Each small bolt weighs 8 grams and each large bolt weighs 15 grams. In one batch the factory produced s small bolts and L large bolts with a total weight of 1200 grams. Which equation represents this situation?
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Why B is right
Since each small bolt weighs 8 grams and s small bolts were produced, the total weight of small bolts is 8s grams. Since each large bolt weighs 15 grams and L large bolts were produced, the total weight of large bolts is 15L grams. The total weight is 8s+15L=1200.
Why the others are wrong
AThis incorrectly swaps the coefficients, associating 15 with small bolts and 8 with large bolts.
CThis incorrectly uses subtraction instead of addition for the large bolt weight.
DThis omits the weight coefficients and only counts the number of bolts.
Question 10Easy
A water tank is being filled according to the equation V=120+15t, where V is the volume of water in gallons and t is the time in minutes since filling began. Which statement is the best interpretation of 15 in this context?
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Why B is right
In the equation V=120+15t, the coefficient 15 is multiplied by t (time in minutes). This means the volume increases by 15 gallons for each minute that passes, so the tank fills at a rate of 15 gallons per minute.
Why the others are wrong
AThis interprets 15 as the initial volume, but the constant term 120 represents the initial volume in the tank.
CThis uses the wrong operation; since 15 is positive and added, the volume increases rather than decreases.
DThis represents an arithmetic slip, misreading 15 as 1.5 by incorrectly placing a decimal point.
Question 11Easy
In the xy-plane, the graph of the equation 2x+5y=30 has a y-intercept at (0, k). What is the value of k?
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Why C is right
The y-intercept occurs when x=0. Substituting x=0 into the equation 2x+5y=30 gives 2(0)+5y=30, which simplifies to 5y=30. Dividing both sides by 5 yields y=6, so k=6.
Why the others are wrong
AThis is the coefficient of x in the equation, not the y-intercept. The y-intercept is found by setting x = 0 and solving for y.
BThis is the coefficient of y in the equation. To find the y-intercept, substitute x = 0 and solve for y, which gives 30/5 = 6.
DThis applies an incorrect sign. When x = 0, the equation 5y = 30 yields a positive value for y, not a negative one.
Question 12Easy
A cyclist travels at a speed of 12 miles per hour on flat terrain and 8 miles per hour on hills. The cyclist travels for f hours on flat terrain and h hours on hills for a combined total of 80 miles. Which equation represents this situation?
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Why D is right
Since the cyclist travels 12 miles per hour for f hours on flat terrain, the distance covered on flat terrain is 12f miles. Since the cyclist travels 8 miles per hour for h hours on hills, the distance covered on hills is 8h miles. The total distance is 12f+8h=80.
Why the others are wrong
AThis omits the speed coefficients for flat terrain and hills.
BThis incorrectly swaps the coefficients, assigning 8 mph to flat terrain and 12 mph to hills.
CThis incorrectly uses 20 (which is 12 + 8) as the coefficient for both variables.
Question 13Easy
A rental car company charges customers using the equation C=45+0.25m, where C is the total charge in dollars and m is the number of miles driven. Which statement is the best interpretation of 0.25 in this context?
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Why A is right
In the equation C=45+0.25m, the coefficient 0.25 is multiplied by m (miles driven). This means for each additional mile, the total charge increases by $0.25, so the company charges $0.25 per mile driven.
Why the others are wrong
BThis interprets 0.25 as the constant term, but the constant term is 45, which represents the fixed fee.
CThis misreads the decimal 0.25 as 25, an arithmetic error in reading the coefficient value.
DThis reverses the operation; since 0.25 is added (positive coefficient), the charge increases rather than decreases with each mile.
Question 14Easy
In the xy-plane, the graph of the equation 6x+2y=24 intersects the y-axis at point P. What is the y-coordinate of point P?
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Why D is right
The graph intersects the y-axis where x=0. Substituting x=0 into the equation gives 6(0)+2y=24, which simplifies to 2y=24, so y=12. The y-coordinate of point P is 12.
Why the others are wrong
AThis is the coefficient of y in the original equation, not the y-coordinate of the intercept.
BThis is the x-intercept value, not the y-intercept value.
CThis results from an incorrect sign when solving for y.
Question 15Easy
A bakery sells cupcakes for $4 each and cookies for $2 each. On a given day, the bakery sold x cupcakes and y cookies for a total of $120. Which equation represents this situation?
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Why C is right
The total revenue is the sum of revenue from cupcakes and cookies. Since cupcakes cost $4 each and the bakery sold x cupcakes, revenue from cupcakes is 4x. Since cookies cost $2 each and the bakery sold y cookies, revenue from cookies is 2y. The total is 4x+2y=120.
Why the others are wrong
AThis incorrectly swaps the coefficients, assigning the cookie price to cupcakes and vice versa.
BThis applies an incorrect sign to the cookie term.
DThis omits the price coefficients entirely, treating all items as having the same value.
Question 16Easy
In the xy-plane, the graph of the equation 8x−2y=16 intersects the y-axis at point Q. What is the y-coordinate of point Q?
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Why D is right
The graph intersects the y-axis where x=0. Substituting x=0 into the equation gives 8(0)−2y=16, which simplifies to −2y=16, so y=−8. The y-coordinate of point Q is -8.
Why the others are wrong
AThis is the x-intercept value, not the y-intercept value.
BThis results from forgetting the negative sign when solving -2y = 16.
CThis is the negative of the coefficient of y, not the y-intercept value.
Question 17Easy
In the xy-plane, the graph of the equation 3x+7y=42 passes through the point (7, p). What is the value of p?
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Why D is right
Substituting x=7 into 3x+7y=42 gives 3(7)+7y=42, which simplifies to 21+7y=42. Solving for y gives 7y=21, so y=3. Therefore p=3.
Why the others are wrong
AThis incorrectly uses the x-coordinate as the y-coordinate.
BThis incorrectly applies a negative sign to the correct answer.
CThis is the result of dividing 42 by 7 without accounting for the 3x term.
Question 18Easy
In the xy-plane, the graph of the equation 4x−3y=24 crosses the x-axis at the point (a, 0). What is the value of a?
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Why D is right
To find the x-intercept, substitute y=0 into the equation. This gives 4x−3(0) = 24, which simplifies to 4x=24. Dividing both sides by 4 yields x=6.
Why the others are wrong
AThis results from incorrectly applying a negative sign when solving for x.
BThis is the negative value of what would be the y-intercept, representing a confusion between axes.
CThis is the coefficient of x in the original equation, not the x-intercept.
Question 19Easy
In the xy-plane, the graph of the equation 2x+5y=20 has a y-intercept at (0, b). What is the value of b?
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Why B is right
To find the y-intercept, substitute x=0 into the equation: 2(0)+5y=20, which gives 5y=20, so y=4. The y-intercept is (0, 4), meaning b=4.
Why the others are wrong
AThis is the coefficient of x in the original equation, not the y-intercept value.
CThis is the coefficient of y in the original equation, not the y-intercept value.
DThis results from an incorrect sign when solving for y.
Question 20Easy
In the xy-plane, the graph of the equation 3x+8y=72 has a y-intercept of (0, b). What is the value of b?
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Why C is right
The y-intercept occurs when x=0. Substituting x=0 into the equation gives 3(0)+8y=72, which simplifies to 8y=72, so y=9. Therefore b=9.
Why the others are wrong
AThis is the coefficient of x in the equation, not the y-intercept.
BThis is the coefficient of y, not the y-intercept value.
DThis results from incorrectly dividing 72 by 3 instead of by 8.
What to do after easy
Getting these right quickly is the point: speed on the easy questions is what buys time for the hard ones. When they stop costing you effort, move up.
Questions are written by SAT Climb and drawn from its own item bank. SAT® is a registered trademark of College Board, which is not affiliated with and does not endorse SAT Climb.