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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.

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.