we need to find the equation of the line from the general equation of the line
[tex]y=mx+b[/tex]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
[tex]m=\frac{y2-y1}{x2-x1}[/tex]where (x2,y2) isa right point from (x1,y1)
I will use the points (100 , 6) and (60 , 12)
replacing
[tex]\begin{gathered} m=\frac{6-12}{100-60} \\ \\ m=\frac{-6}{40}=-0.15 \end{gathered}[/tex]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)
[tex]\begin{gathered} y=mx+b \\ (6)=(-0.15)(100)+b \\ 6=-15+b \\ b=6+15 \\ b=21 \end{gathered}[/tex]b or y-intercept is 21
then replacing slope and b on general equation we have the expression of the line
[tex]\begin{gathered} y=mx+b \\ \\ y=-0.15x+21 \end{gathered}[/tex]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
[tex]\begin{gathered} y=-0.15x+21 \\ \\ y=-0.15(75)+21 \\ y=-11.25+21 \\ y=5.75 \end{gathered}[/tex]people to 75° is 5.75(thousands)
now we do a subtract between the people of each temperature
[tex]6-5.75=0.25[/tex]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
