Question

explore - part 1
the scatter plot for the data on ice cream sales is shown. we need to estimate a line of best fit for the data.

1. choose any two points that look like they would be on a line through the data.
2. use the two points to calculate the slope and y - intercept in desmos. (hint: create a table with just the two points you selected in part 1, then create a linear regression)

slope = y - intercept=

1. what does the slope suggest in the context of the problem?
2. what is the equation of the line of best fit?

Explanation:

Step1: Select two points

Let's choose the points \((60,60)\) and \((80,120)\) (Note: These are sample points, other valid points can also be chosen depending on visual inspection of the scatter - plot).

Step2: Calculate the slope

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
For the points \((x_1,y_1)=(60,60)\) and \((x_2,y_2)=(80,120)\), we have \(m=\frac{120 - 60}{80 - 60}=\frac{60}{20}=3\).

Step3: Calculate the y - intercept

Using the point - slope form \(y - y_1=m(x - x_1)\), substituting \(m = 3\), \(x_1=60\) and \(y_1 = 60\).
\(y-60=3(x - 60)\)
\(y-60=3x-180\)
\(y=3x- 120\), so the \(y\) - intercept \(b=-120\).

Step4: Interpret the slope

The slope \(m = 3\) means that for every 1 - degree Fahrenheit increase in temperature, the ice - cream sales increase by 3 dollars.

Step5: Write the equation of the line

The equation of a line in slope - intercept form is \(y=mx + b\). Substituting \(m = 3\) and \(b=-120\), we get \(y = 3x-120\).

Answer:

1. \((60,60)\) and \((80,120)\) (other valid pairs are possible)
2. Slope \(=3\), \(y\) - intercept \(=-120\)
3. For every 1 - degree Fahrenheit increase in temperature, ice - cream sales increase by 3 dollars.
4. \(y = 3x-120\)