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Drill by score band: 400–500 500–600 600–700 700–800

Score band 400-500 · Heart of Algebra

Linear Functions and Their Graphs drills for 400-500

400500600700800

Targeted practice for students currently scoring in the 400-500 range, drilling exclusively on linear functions and their graphs.

What a 400-500 scorer needs from this topic

The 400 to 500 score band on SAT Math is the foundations band. Students scoring here are usually strong on arithmetic but losing easy points to careless setup, missed units, or an unfamiliar SAT phrasing of a familiar idea. Drilling the foundations questions here is the highest leverage thing you can do for your score, because every problem you convert from a guess to a confident solve moves you a measurable number of scaled points. Foundations questions in this band test one idea at a time, with friendly numbers and short stems. Treat them as warmups for the rest of the section: do them untimed first, write every step on paper, and check that your final value answers the actual question being asked, not the value of x.

For Linear Functions and Their Graphs specifically, students in the 400-500 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 400-500 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. 400-500 easy Slope and y-Intercept Interpretation

    A gym charges a monthly fee of $34 plus $5 per visits. Which equation gives the total cost y for x visits?

    1. A y = 39x
    2. B y = 5x - 34
    3. C y = 5x + 34
    4. D y = 34x + 5
    Worked solution

    Answer: C — y = 5x + 34

    The fixed monthly fee of $34 is the y-intercept (the cost when x = 0). The per-visits rate $5 is the slope (the change per unit of x). Combining them gives y = 5x + 34. Sanity check: at x = 11, y = 5(11) + 34 = 89.

  2. 400-500 easy Parallel and Perpendicular Slopes

    A plumber charges a service call fee of $22 plus $9 per hours. Which equation gives the total bill y for x hours?

    1. A y = 9x - 22
    2. B y = 22x + 9
    3. C y = 31x
    4. D y = 9x + 22
    Worked solution

    Answer: D — y = 9x + 22

    The fixed service call fee of $22 is the y-intercept (the cost when x = 0). The per-hours rate $9 is the slope (the change per unit of x). Combining them gives y = 9x + 22. Sanity check: at x = 20, y = 9(20) + 22 = 202.

  3. 400-500 easy Writing Equations from Points and Slopes

    A phone plan charges a monthly base of $14 plus $13 per gigabytes used. Which equation gives the monthly bill y for x gigabytes used?

    1. A y = 13x + 14
    2. B y = 27x
    3. C y = 13x - 14
    4. D y = 14x + 13
    Worked solution

    Answer: A — y = 13x + 14

    The fixed monthly base of $14 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 + 14. Sanity check: at x = 3, y = 13(3) + 14 = 53.

  4. 400-500 easy Building Linear Functions from Tables

    A rideshare charges a pickup fee of $50 plus $8 per miles. Which equation gives the fare y for x miles?

    1. A y = 58x
    2. B y = 8x - 50
    3. C y = 50x + 8
    4. D y = 8x + 50
    Worked solution

    Answer: D — y = 8x + 50

    The fixed pickup fee of $50 is the y-intercept (the cost when x = 0). The per-miles rate $8 is the slope (the change per unit of x). Combining them gives y = 8x + 50. Sanity check: at x = 17, y = 8(17) + 50 = 186.

  5. 400-500 easy Slope and y-Intercept Interpretation

    A printer charges a setup charge of $22 plus $14 per pages. Which equation gives the order cost y for x pages?

    1. A y = 14x - 22
    2. B y = 14x + 22
    3. C y = 36x
    4. D y = 22x + 14
    Worked solution

    Answer: B — y = 14x + 22

    The fixed setup charge of $22 is the y-intercept (the cost when x = 0). The per-pages rate $14 is the slope (the change per unit of x). Combining them gives y = 14x + 22. Sanity check: at x = 13, y = 14(13) + 22 = 204.

  6. 400-500 easy Parallel and Perpendicular Slopes

    A gym charges a monthly fee of $15 plus $5 per visits. Which equation gives the total cost y for x visits?

    1. A y = 20x
    2. B y = 5x - 15
    3. C y = 15x + 5
    4. D y = 5x + 15
    Worked solution

    Answer: D — y = 5x + 15

    The fixed monthly fee of $15 is the y-intercept (the cost when x = 0). The per-visits rate $5 is the slope (the change per unit of x). Combining them gives y = 5x + 15. Sanity check: at x = 6, y = 5(6) + 15 = 45.

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 400-500 drills