Back to Exercise: Interpret slope and intercept of a linear model

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

Printable layout

Warm-Up: Identify Slope and Intercept

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

A linear model is written $y = a + bx$ . In the savings model $y = 200 + 50x$ (where $x$ is months and $y$ is dollars), which number is the slope and which is the intercept?

The slope is $50$ and the intercept is $200$ .

The slope is $200$ and the intercept is $50$ .

The slope is $x$ and the intercept is $y$ .

Both $50$ and $200$ are slopes.

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.

A model gives $y = 50x + 200$ for a savings account, where $x$ is months and $y$ is dollars. According to the model, what is the predicted balance (in dollars) when $x = 0$ ? ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲

Fluency Practice

Interpret each slope or intercept as a sentence with units.

$Scatter plot of cost versus minutes with a rising fitted line; a dashed step shows a one-unit increase in x raising y by b.$

The scatter plot below shows a phone bill versus minutes used, with a fitted line $y = a + bx$ . The dashed step shows that moving $1$ unit to the right on $x$ raises $y$ by $b$ . Which is the best interpretation of the slope $b = 0.10$ ?

For each additional minute used, the predicted bill increases by $\text{\char"0024}0.10$ .

The bill is $\text{\char"0024}0.10$ in total.

When $x = 0$ the bill is $\text{\char"0024}0.10$ .

The slope is just $0.10$ with no further meaning.

A model gives $y = 0.10x + 20$ for a phone bill (dollars) versus minutes. By how many dollars does the predicted bill change when minutes increase by exactly $1$ ? ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲

A car's value is modeled by $y = -2000x + 24000$ , where $x$ is age in years and $y$ is value in dollars. Which is the best interpretation of the slope $-2000$ ?

The car loses $\text{\char"0024}2000$ in value for each additional year of age.

There is no relationship between age and value, because the slope is negative.

The car gains $\text{\char"0024}2000$ in value each year.

The car is worth $-\text{\char"0024}2000$ .

A candle's height is modeled by $y = -3x + 90$ , where $x$ is minutes burning and $y$ is height in cm. What is the candle's predicted height (in cm) at the start, when $x = 0$ ? ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲

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