Question

the table shows the numbers of ice cream cones sold for different outside temperatures (in degrees fahrenheit).
temperature, x 53 62 70 82 90
number of cones, y 90 105 117 131 147
do the data show a linear relationship?
yes
no
if the data show a linear relationship, write an equation of a line of fit using the ordered pairs (62, 105) and (70, 117). then use the equation to estimate how many ice cream cones are sold when the temperature is 60°f. if the data do not show a linear relationship, leave the following blank.
an equation is y =
about ice cream cones are sold when the temperature is 60°f.

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(62,105)$ and $(70,117)$, we have $m=\frac{117 - 105}{70 - 62}=\frac{12}{8} = 1.5$.

Step2: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(62,105)$ and $m = 1.5$. So $y-105=1.5(x - 62)$. Expand to get $y-105=1.5x-93$. Then $y=1.5x + 12$.

Step3: Estimate the number of cones

Substitute $x = 60$ into $y=1.5x + 12$. So $y=1.5\times60+12=90 + 12=102$.

To check linearity, as the temperature $x$ increases, the number of cones $y$ increases at a relatively constant rate. For example, from $x = 53$ to $x = 62$ (increase of 9), $y$ goes from 90 to 105 (increase of 15); from $x = 62$ to $x = 70$ (increase of 8), $y$ goes from 105 to 117 (increase of 12) etc. The data shows a linear relationship.

Answer:

Yes
An equation is $y = 1.5x+12$
About 102 ice - cream cones are sold when the temperature is $60^{\circ}F$.