SAT Graphing Linear Functions Practice Questions (Free + Explanations)

Algebra · Graphing Linear Functions

SAT Graphing Linear Functions Practice Questions (Free + Explanations) | Quiz 1

Question 12345 of 5

Question 1 of 5

A gym charges a one-time sign-up fee of 25 and then 15 per month. If y represents the total cost, in dollars, after x months, which graph represents this relationship?

Explanation The total cost starts at 25 before any months have passed, so the graph must have a y -intercept of 25 . The cost increases by 15 for each month, so the slope is 15 . Therefore, the correct graph is the line with y -intercept 25 and slope 15 . Concept summary In a linear model, the y -intercept is the starting amount and the slope is the amount added for each unit of x .

Question 2 of 5

The graph of the line y = - 3 x + 5 is shown in the x y -plane. What is the y -coordinate of the point on the line where x = 2 ?

Explanation Substitute x = 2 into y = - 3 x + 5 : y = - 3 (2) + 5 = - 6 + 5 = - 1 So the y -coordinate is - 1 . Concept summary For a line written as y = m x + b, you can find the point's y -value by substituting the given x -value into the expression.

Question 3 of 5

The graph of the line y = 3 x - 4 is rewritten in the form y = 3 (x - a) . What is the value of a ?

Explanation To make y = 3 x - 4 look like y = 3 (x - a), expand the second form: y = 3 (x - a) = 3 x - 3 a . Since this must equal 3 x - 4, set - 3 a = - 4 . Solving gives a = \frac{4}{3} . Concept summary Equivalent forms of a linear function can be found by factoring. When a coefficient is factored out, the number inside the parentheses changes accordingly.

Question 4 of 5

A line passes through the points (2, 5) and (6, 13) . What is the slope of the line?

ExplanationUse the slope formula:For the points and ,So the slope of the line is .Concept summaryTo find the slope from two points, divide the vertical change by the horizontal change:\frac{\Delta y}{\Delta x}}.

Question 5 of 5

Line k passes through the point (0, 4) and intersects the line y = x at the point (2, 2) . What is the equation of line k ?

Explanation Line k goes through (0, 4) and (2, 2) . Its slope is \frac{2 - 4}{2 - 0} = \frac{- 2}{2} = - 1 . Since the line passes through (0, 4), its y -intercept is 4 . Therefore, the equation is y = - x + 4 . Concept summary To write the equation of a line from two points, find the slope using change in y over change in x, then use the point with x = 0 to identify the y -intercept.

Your results

0of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Your results

1of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Your results

2of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Your results

3of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Your results

4of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Your results

5of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Practice outline (enable JavaScript for interactive mode)

Q1. A gym charges a one-time sign-up fee of 25 and then 15 per month. If y represents the total cost, in dollars, after x months, which graph represents this relationship?

Q2. The graph of the line y = − 3 x + 5 is shown in the x y -plane. What is the y -coordinate of the point on the line where x = 2 ?

Q3. The graph of the line y = 3 x − 4 is rewritten in the form y = 3 ( x − a ) . What is the value of a ?

Q4. A line passes through the points ( 2 , 5 ) and ( 6 , 13 ) . What is the slope of the line?

Q5. Line k passes through the point ( 0 , 4 ) and intersects the line y = x at the point ( 2 , 2 ) . What is the equation of line k ?