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4-42.

Fabienne compared annual grocery bills with the other mothers at her church. She discovered a linear relationship between the total cost (in dollars) of groceries and the number of miles the mother lived from the downtown church. 4-42 HW eTool (Desmos) Homework Help ✎

1. Do you think that the association would be positive or negative? Strong or weak?

Recall the standards for a weak/strong association.

2. The upper boundary for Fabienne’s prediction was modeled by $g = 11.27 - 0.14d$, where $g$ is the cost of groceries (in thousands of dollars) and $d$ is the distance from church (miles). The lower boundary was $g = 7.67 - 0.14d$. Estimate the equation of Fabienne’s line of best fit.

The y-intercept should be approximately halfway between $11.27$ and $7.67$.
(Find a number that is halfway).

$g = 9.47 − 0.14d$

3. Interpret the slope of Fabienne’s model in context.

The slope is represented by $-0.14$ in the equation, but remember that we are working in thousands of dollars, so it would be $140$.
What is the slope saying about the cost in relation to the number of miles?

4. Fabienne lives $8$ miles from church. Her residual was $510$. About how much did she spend on groceries this year?

• Substitute $8$ in for $d$ and evaluate.
Add the residual of $510$ to find the actual amount that she is paying.