Part A) What is the equation of the line, written in slope-intercept form? Show how you determined the equation.
Considering the point-slope form of a linear equation
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}\:\left(x-x_1\right)[/tex]
Given the points from the line in the diagram
Substituting the values in the point-slope formula
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}\:\left(x-x_1\right)[/tex]
[tex]y-10=\frac{15-10}{2-6}\:\left(x-6\right)[/tex]
[tex]y-10=-\frac{5}{4}\left(x-6\right)[/tex]
[tex]y-10+10=-\frac{5}{4}\left(x-6\right)+10[/tex]
[tex]y=-\frac{5}{4}x+\frac{35}{2}[/tex]
Therefore, [tex]y=-\frac{5}{4}x+\frac{35}{2}[/tex] is the equation of the line, written in slope-intercept form.
The graph of the equation [tex]y=-\frac{5}{4}x+\frac{35}{2}[/tex] is also attached below.
Part 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.
As we have determined the equation
[tex]y=-\frac{5}{4}x+\frac{35}{2}[/tex]
Putting x = 0 in the above equation
[tex]y=-\frac{5}{4}\left(0\right)+\frac{35}{2}[/tex]
[tex]\:y\:=\frac{35}{2}[/tex]
Thus, Anika worked for [tex]\frac{35}{2}[/tex] hours on the set up crew on the day the fair arrived at the fairgrounds day 0.
Part C) Approximately how much did her setup time decrease per day?
Now, we have to mention decrease per day which is equal to the slope of line.
As we know the equation
[tex]y=-\frac{5}{4}x+\frac{35}{2}[/tex]
comparing it with slope-intercept form in order to find the slop
As the slope-intercept form is
[tex]y=mx+b[/tex]
[tex]y=-\frac{5}{4}x+\frac{35}{2}[/tex]
[tex]\:m=\frac{-5}{4}[/tex]
Therefore, [tex]\:m=\frac{-5}{4}[/tex] is the decrease per day.
Keywords: slope-intercept form, slope, equation
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