Question

The scatter shows the number of people at a fair based on the outside temperature. How many fewer people would be predicted to be at the fair on a 100°F day than on a 75°F day? I got -0.16 as the slope but im not sure how to get this. For each degree that the outside temperature increases, the fair attendance decreases by _____ thousand people. (integer or decimal)

Answer 1

we need to find the equation of the line from the general equation of the line

`y=mx+b`

where m is the slope and b the y-intercept

Slope

We use two points of the line to find the slope by the formula

`m=(y2-y1)/(x2-x1)`

where (x2,y2) isa right point from (x1,y1)

I will use the points (100 , 6) and (60 , 12)

replacing

`\begin{gathered} m=(6-12)/(100-60) \\ \\ m=(-6)/(40)=-0.15 \end{gathered}`

the slope is -0.15

Y-intercept

we replace the value of the slope and a point of the line, on general equation to solve b

I will use the point (100 , 6)

`\begin{gathered} y=mx+b \\ (6)=(-0.15)(100)+b \\ 6=-15+b \\ b=6+15 \\ b=21 \end{gathered}`

b or y-intercept is 21

then replacing slope and b on general equation we have the expression of the line

`\begin{gathered} y=mx+b \\ \\ y=-0.15x+21 \end{gathered}`

How many fewer people would be predicted to be at the fair on a 100°F day than on a 75°F day?

people to 100° is 6(thousands)

to find people to 75° we replace 75 on the fuction of the line

`\begin{gathered} y=-0.15x+21 \\ \\ y=-0.15(75)+21 \\ y=-11.25+21 \\ y=5.75 \end{gathered}`

people to 75° is 5.75(thousands)

now we do a subtract between the people of each temperature

`6-5.75=0.25`

there will be 0.25(thousands) more people or 250

For each degree that the outside temperature increases, the fair attendance decreases by _____ thousand people.

the slope tells us how much a value changes for each unit

then the blank is 0.15

we dont use negative sign because the statement says "decreases", so we are talking about negative value