Question

Jack plotted the graph below to show the relationship between the temperature of his city and the number of ice cream cones he sold daily: Main title on graph is Ice Cream Cone Sale. Graph shows 0 to 30 on x axis at increments of 5 and 0 to 60 on y axis at increments of 10. The label on the x axis is Temperature in degree C, and the label on the y axis is Number of Ice Cream Cones Sold. Dots are made at the ordered pairs 0, 5 and 5, 15 and 7.5, 15 and 10, 24 and 10, 28 and 12, 32 and 12.5, 25 and 12.5, 30 and 15, 35 and 15, 40 and 17.5, 35 and 20, 45 and 22.5, 36 and 23, 46 and 25, 55 and 27.5, 60. Part A: In your own words, describe the relationship between the temperature of the city and the number of ice cream cones sold. (5 points) Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate slope and y-intercept. (5 points)

Answer 1

(a) The amount of ice cream increase as temperature increases

(b)

`y = 2x + 5` --- equation

`y = 5` --- y intercept

`m = 2` --- slope

Explanation:

Given

See attachment for graph

Solving (a): The relationship between the variables

From the attached graph, the dots on the graph increases towards up-right direction. This implies that there is a positive correlation between the variables.

In other words;

The amount of ice cream increase as temperature increases

Solving (b): The line of best fit

First, we draw a line through the points (the line should have almost equal points on both sides; see attachment 2).

From (2), we select any 2 points on the line:

`(x_1,y_1) = (15,35)`

`(x_2,y_2) = (0,5)`

The slope (m) is:

`m = (y_2 -y_1)/(x_2 - x_1)`

`m = (5-35)/(0-15)`

`m = (-30)/(-15)`

`m = 2`

So, the line of best fit is:

`y = m(x - x_1) + y_1`

Substitute known values:

`y = 2(x - 0) + 5`

`y = 2(x) + 5`

`y = 2x + 5`

The y-intercept is when
`x=0`

So, we have:

`y = 2*0 + 5`

`y = 0 + 5`

`y = 5`