is the same as picking from a points set hmmm, notice the table is an x,y table, so we can just pick any two points to get the slope and thereby the equation.
3)
let's use (100, 36.5) and (300, 106.5)
[tex] \bf (\stackrel{x_1}{100}~,~\stackrel{y_1}{36.5})\qquad
(\stackrel{x_2}{300}~,~\stackrel{y_2}{106.5})
\\\\\\
slope = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{106.5-36.5}{300-100}\implies \cfrac{70}{200}\implies \cfrac{7}{20}
\\\\\\
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-36.5=\cfrac{7}{20}(x-100)
\\\\\\
y-36.5=\cfrac{7}{20}x-35\implies y=\cfrac{7}{20}x+1.5 [/tex]
4)
and for this one let's pick say (35, 88) and (45, 82)
[tex] \bf (\stackrel{x_1}{35}~,~\stackrel{y_1}{88})\qquad
(\stackrel{x_2}{45}~,~\stackrel{y_2}{82})
\\\\\\
slope = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{82-88}{45-35}\implies \cfrac{-6}{10}\implies -\cfrac{3}{5}
\\\\\\
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-88=-\cfrac{3}{5}(x-35)
\\\\\\
y-88=-\cfrac{3}{5}x+21\implies y=-\cfrac{3}{8}x+109 [/tex]
