Use both changes in a table
For points (2, 11) and (5, 23), the output increases by 12 while the input increases by 3. The slope is 12/3 = 4, not 12. Slope describes a one-unit input change, even if the table skips several input values between rows.
Find the starting value by substituting a point into y = mx + b. Using (2, 11) and m = 4 gives 11 = 8 + b, so b = 3. The model y = 4x + 3 predicts 23 when x = 5, matching the second row. That substitution is an inexpensive error check.
Separate the setup fee from the hourly charge
A rental service might charge a fixed fee plus an hourly rate. If the rate is $6 per hour and a four-hour rental costs $31, the hourly part is $24 and the fixed fee is $7. In C = 6h + 7, the slope has units of dollars per hour; the intercept has units of dollars.
Do not divide the entire bill by the number of hours and call the result the hourly rate when a fixed fee is present. That quotient is the average cost per hour for that particular rental, a different quantity. Reading the wording before calculating prevents this common confusion.
Ask whether the pattern adds or multiplies
Equal input steps in a linear model produce equal output differences. Equal input steps in an exponential model produce equal output ratios, when the ratio is defined. Values 10, 15, 20, 25 have a constant difference of 5. Values 10, 20, 40, 80 have a constant ratio of 2.
For y = 100(1.2)ᵗ, the factor 1.2 means retaining the previous amount and adding 20% of that amount. Two steps give 144, not 140. In a decay model with factor 0.85, the retained portion is 85% and the reduction is 15%. The starting amount does not change that percentage.
Choose a method that matches the model
A polynomial graph workspace is useful for lines and quadratics. It cannot directly plot a general exponential expression. For growth questions, repeated multiplication, exact substitution, or the official testing calculator is the appropriate tool. Entering an exponential model as a quadratic would produce the wrong curve even if a few values looked similar.
After a mixed set, use the topic breakdown to choose your next practice session. Missed intercept questions suggest revisiting the fixed-fee example. Missed growth questions suggest checking factors and exponents. This small bank measures how you handled these exercises; it does not estimate an SAT section score or cover every kind of data-analysis question.
Put the idea into practice.
Try eight original questions with explanations after each answer.
Practice this skill →References and further practice
- College Board: SAT Math overview
- College Board: official full-length practice
- Desmos: testing calculators
References establish the test context. The examples and teaching explanations here are original. See our methodology for coverage and limitations.