Back to Exercise: Use the equation of a linear model to solve problems in the context of bivariate measurement data

Exercises: Linear Models -- Equation, Slope, Intercept, and Predictions

Work through each section in order. For interpretation problems, use complete sentences with units and the phrase "associated with" rather than "causes."

Grade 8·27 problems·~35 min·Common Core Math - Grade 8·container·8-sp-a-3

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Recall / Warm-Up

A line passes through the points $(2, 9)$ and $(6, 21)$ . What is its slope?

$3$

$\frac{1}{3}$

$12$

$4$

For the line $y = 4x + 7$ , what is the slope?

For the line $y = 4x + 7$ , what is the value of $y$ when $x = 0$ (the y-intercept)?

Fluency Practice

$Scatter plot of plant height versus hours of sunlight with a rising line of fit through the points (3, 15) and (9, 24)$

A line of fit on a scatter plot passes through the points $(3, 15)$ and $(9, 24)$ . What is the slope of this line?

A line of fit passes through $(3, 15)$ with slope $1.5$ . Find the y-intercept $b$ so the equation has the form $y = 1.5x + b$ .

A linear model for a biology experiment is $y = 1.5x + 10.5$ , where $x$ is hours of daily sunlight and $y$ is mature plant height in cm. Interpret the slope in context using a complete sentence with units.

A model relating a car's age in years ( $x$ ) to its resale price in thousands of dollars ( $y$ ) is $y = -1.8x + 28$ . Interpret the slope in context, including what the negative sign means.

Using the plant model $y = 1.5x + 10.5$ (with $x$ in hours of sunlight and $y$ in cm), predict the plant height when $x = 6.5$ hours.

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