3. Anika is on the crew to set up rides for the state fair. The crew does most of the setup on the day that the fair arrives at the fairground and then continues to work on finishing the setup for about a week to have the rides ready to go in time for the opening of the fair. The scatter plot shows Anika's setup time on different days and the linear model for the data.(a) What is the equation of the line, written in slope-intercept form? Show how you determined the equation.(b) Based on the linear model, predict how long Anika worked on the setup crew on the day the fair arrived at the fairgrounds, Day 0. Approximately how much did her setup time decrease per day?Answer:

a) To find the equation of the line, take the two points and find the slope.
(2, 15), (7, 8)x1  y1   x2 y2






So the slope of the line is -7/5. Now let's plug that in along with one of the points into slope-intercept form.


Where 'm' is the slope and  is a point on the line. Let's use the point (7, 8).


Now we can distribute -7/5 into the parenthesis to get it into slope-intercept form:


Now add 8 to both sides:


So this is our equation in slope-intercept form.
(b)
How long Anita worked on Day 0 is the same thing as the y-intercept of our equation, 17.8, which means she worked 17.8 hours on Day 0. The value at which her setup time decreased per day is the same as the slope, -7/5, which means it decreased by 7/5 each day.