8.SP.A.3: Use the equation of a linear model to solve problems in the context of bivariate… — Practice

Work through problems with immediate feedback

Concepts

A linear model relating hours of daily sunlight to plant height
has a slope of 1.5. A student says, "The slope means the plant
is 1.5 cm tall." Is the student's interpretation correct?

Yes -- the slope directly tells you the plant's height

No -- the slope tells you how much the predicted height changes for each additional hour of sunlight, not the height itself

Yes, but only when x = 1

No -- the slope only applies to negative associations

A linear model relating car age (years) to resale price
(dollars) is y = -1800x + 28000. Which sentence correctly
interprets the slope in context?

For each additional year of age, the predicted resale price is associated with a decrease of $1,800

The car is worth $1,800

For each additional year of age, the predicted resale price is associated with an increase of $1,800

A car that is 1,800 years old would be worth $0

A linear model relates a person's age (x, in years, with data
collected from ages 25 to 65) to annual salary (y, in
thousands of dollars): y = 1.2x + 8. A student says, "The
y-intercept of 8 means a newborn (age 0) is predicted to earn
$8,000 per year, and that's a perfectly meaningful prediction."
Is the student correct?

Yes -- the y-intercept always gives a meaningful real-world value

Yes, because $8,000 is a small, reasonable-sounding number

No -- linear models never have meaningful y-intercepts

No -- x = 0 is far outside the data range (ages 25-65) and does not make sense in this context, so the y-intercept is not a meaningful prediction here

Procedures

A fitted line for absences (x) versus exam score (y) passes
through the points (0, 95) and (10, 55). What is the slope of
this line?

A linear model is y = -4x + 95, where x is number of absences
and y is predicted exam score. The data used to build this model
covered students with 0 to 12 absences. What exam score does the
model predict for a student with 6 absences?

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Linear Models -- Tutor Intake Assessment

Concepts

Procedures