Back to Interpret slope and intercept of a linear model — Problem 2 · Task Set 9

Exercises: Interpret the Slope and Intercept of a Linear Model

Work through each section in order. For every interpretation, write a full sentence about the real situation and include UNITS. Remember: the slope is a rate of change (y-units per x-unit) and the intercept is the predicted value when x = 0 (in y-units) — but the intercept is only meaningful when x = 0 is realistic and near the data.

Grade 9·20 problems·~35 min·Common Core Math - HS Statistics and Probability·group·hss-id-c-7

Work through problems with immediate feedback

Warm-Up: Identify Slope and Intercept

These problems review identifying a and b in y = a + bx.

A model gives $y = 0.10x + 20$ for a phone bill, where $x$ is minutes and $y$ is dollars. A student writes "the slope is $0.10$ ." Why is this interpretation incomplete?

It states a bare number; a slope interpretation must include units and a sentence, e.g. "the bill rises $\text{\char"0024}0.10$ for each additional minute."

The slope should be written as a percent, $10\%$ .

The slope is actually $20$ , not $0.10$ .

Nothing is wrong; "the slope is $0.10$ " is a complete interpretation.