Question

question 5 of 6 (1 point) | question attempt: 1 of unlimited the scatter plot shows the average monthly temperature, x, and the monthly heating cost of a family, y, for 24 different months. use the equation of the line of best fit, y = - 1.21x + 96.10, to answer the questions below. give exact answers, not rounded approximations. (a) for an increase of one degree fahrenheit, what is the predicted decrease in the monthly heating cost? (b) what is the predicted heating cost for a month with an average temperature of 0 °f? (c) what is the predicted heating cost for a month with an average temperature of 35 °f?

Explanation:

Step1: Analyze slope for part (a)

The slope of the line $y = - 1.21x+96.10$ is -1.21. For a linear - equation $y = mx + b$, the slope $m$ represents the change in $y$ for a unit change in $x$. Here, $x$ is the temperature and $y$ is the heating cost. So for an increase of one - degree Fahrenheit ($\Delta x = 1$), the change in $y$ is $\Delta y=m\times\Delta x=-1.21\times1=-1.21$. The negative sign indicates a decrease.

Step2: Substitute $x = 0$ for part (b)

Substitute $x = 0$ into the equation $y=-1.21x + 96.10$. Then $y=-1.21\times0 + 96.10=96.10$.

Step3: Substitute $x = 35$ for part (c)

Substitute $x = 35$ into the equation $y=-1.21x + 96.10$. So $y=-1.21\times35+96.10=-42.35 + 96.10 = 53.75$.

Answer:

(a) $\$1.21$
(b) $\$96.10$
(c) $\$53.75$