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Score band 700-800 · Heart of Algebra

Linear Functions and Their Graphs drills for 700-800

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Targeted practice for students currently scoring in the 700-800 range, drilling exclusively on linear functions and their graphs.

What a 700-800 scorer needs from this topic

The 700 to 800 band is the elite tier of SAT Math. Reaching it requires zero careless errors and confident solves on the hardest one or two questions in each module. Mastery-band drills focus on the hardest released questions: multi-concept problems that combine two or three skills in one stem, abstract algebraic manipulation with parameters instead of numbers, geometry questions that require a clever construction, and data-analysis questions that test conceptual understanding rather than computation. At this level, speed matters as much as accuracy, because the only way to leave time for the hardest questions is to dispatch the easy and medium ones in well under a minute each.

For Linear Functions and Their Graphs specifically, students in the 700-800 band need to focus on the question patterns the College Board uses at this difficulty level. Interpret slope, intercepts, and the meaning of linear functions in context. The questions below are pulled from the ScoreReady question bank and filtered to the 700-800 band based on difficulty calibration that matches publicly released College Board practice materials.

Drill these untimed first. Once you can produce a clean worked solution on paper for every question without notes, switch to timed mode and aim for under 75 seconds per question. That pace is roughly the average time per question on the actual SAT Math section, and it leaves time for the harder questions you will see at the end of each module.

Practice set

  1. 700-800 hard Building Linear Functions from Tables

    A printer charges a setup charge of $28 plus $6 per pages. Which equation gives the order cost y for x pages?

    1. A y = 6x - 28
    2. B y = 6x + 28
    3. C y = 34x
    4. D y = 28x + 6
    Worked solution

    Answer: B — y = 6x + 28

    The fixed setup charge of $28 is the y-intercept (the cost when x = 0). The per-pages rate $6 is the slope (the change per unit of x). Combining them gives y = 6x + 28. Sanity check: at x = 17, y = 6(17) + 28 = 130.

  2. 700-800 hard Slope and y-Intercept Interpretation

    A gym charges a monthly fee of $24 plus $8 per visits. Which equation gives the total cost y for x visits?

    1. A y = 8x - 24
    2. B y = 32x
    3. C y = 24x + 8
    4. D y = 8x + 24
    Worked solution

    Answer: D — y = 8x + 24

    The fixed monthly fee of $24 is the y-intercept (the cost when x = 0). The per-visits rate $8 is the slope (the change per unit of x). Combining them gives y = 8x + 24. Sanity check: at x = 3, y = 8(3) + 24 = 48.

  3. 700-800 hard Parallel and Perpendicular Slopes

    A plumber charges a service call fee of $22 plus $11 per hours. Which equation gives the total bill y for x hours?

    1. A y = 11x - 22
    2. B y = 22x + 11
    3. C y = 33x
    4. D y = 11x + 22
    Worked solution

    Answer: D — y = 11x + 22

    The fixed service call fee of $22 is the y-intercept (the cost when x = 0). The per-hours rate $11 is the slope (the change per unit of x). Combining them gives y = 11x + 22. Sanity check: at x = 11, y = 11(11) + 22 = 143.

  4. 700-800 hard Writing Equations from Points and Slopes

    A phone plan charges a monthly base of $21 plus $13 per gigabytes used. Which equation gives the monthly bill y for x gigabytes used?

    1. A y = 21x + 13
    2. B y = 13x - 21
    3. C y = 34x
    4. D y = 13x + 21
    Worked solution

    Answer: D — y = 13x + 21

    The fixed monthly base of $21 is the y-intercept (the cost when x = 0). The per-gigabytes used rate $13 is the slope (the change per unit of x). Combining them gives y = 13x + 21. Sanity check: at x = 4, y = 13(4) + 21 = 73.

  5. 700-800 hard Building Linear Functions from Tables

    A rideshare charges a pickup fee of $22 plus $5 per miles. Which equation gives the fare y for x miles?

    1. A y = 5x + 22
    2. B y = 22x + 5
    3. C y = 5x - 22
    4. D y = 27x
    Worked solution

    Answer: A — y = 5x + 22

    The fixed pickup fee of $22 is the y-intercept (the cost when x = 0). The per-miles rate $5 is the slope (the change per unit of x). Combining them gives y = 5x + 22. Sanity check: at x = 7, y = 5(7) + 22 = 57.

  6. 700-800 hard Slope and y-Intercept Interpretation

    A printer charges a setup charge of $18 plus $3 per pages. Which equation gives the order cost y for x pages?

    1. A y = 3x - 18
    2. B y = 3x + 18
    3. C y = 18x + 3
    4. D y = 21x
    Worked solution

    Answer: B — y = 3x + 18

    The fixed setup charge of $18 is the y-intercept (the cost when x = 0). The per-pages rate $3 is the slope (the change per unit of x). Combining them gives y = 3x + 18. Sanity check: at x = 17, y = 3(17) + 18 = 69.

How to use these drills to climb a band

Climbing from one score band to the next requires a different study mix than climbing within a band. Within a band, you are mostly fixing careless errors and pattern-recognizing the question types you already understand. Climbing to the next band means adding new question types to your toolbox — patterns you currently recognize but cannot solve fluently. The 700–800 set in this drill is exactly that toolbox for students currently in the 600–700 range.

The single most reliable indicator that you are ready to move up a band is being able to explain a worked solution to someone else, in your own words, without referring to notes. Practice this with one classmate or one parent per week. The act of teaching exposes the gaps your timed solves did not.

Other 700-800 drills