Scott works as a delivery person for a shipping company. the graph shows a linear model for his delivery times on different days.
(a)what is the equation of the line, first written in point-slope form and then written in slope-intercept form? show how you determined the equation.
(b)based on the linear model, predict how long it initially took scott to deliver his packages. approximately how much did his delivery time decrease per day?

We can extract the points (3, 21) and (6, 12) from the graph.

First we are going to find the slope of the line passing through those points. To do it, we are using the slope formula:

where

is the slope of the line

are the coordinates of the first point

are the coordinates of the second point

Our first point is (3, 21) and our second point is (6, 12), so let's replace the values

Now, to find the equation of the line in point, slope, we are using the point-slope formula:

where

is the slope of the line

are the coordinates of the first point.

Since we have the slope, let's replace the values:

Next, to find the equation in slope-intercept form, we just need to solve our point-slope equation for :

Answer

Equation of the line in point-slope form:

Equation of the line in slope-intercept form:

The time that initially took Scoot  to deliver his packages is the time it took him to deliver the packages in his first day of work. In the hist day of word, zero days has passed since he begin working, so .

It initially took Scoot 30 minutes to deliver his packages.

Now, since the slope of our line is negative 3, Scott's delivery time decreases 3 minutes per day.

Answer

It initially took Scoot 30 minutes to deliver his packages.

Scott's delivery time decreases 3 minutes per day.

ok thats very interesting

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.