Answer:
The linear equation in the slope-intercept form will be:
[tex]y\:=\:\frac{2}{3}x+64[/tex]
Step-by-step explanation:
From the line graph, taking two points
Finding the slope between (21, 78) and (27, 82)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(21,\:78\right),\:\left(x_2,\:y_2\right)=\left(27,\:82\right)[/tex]
[tex]m=\frac{82-78}{27-21}[/tex]
[tex]m=\frac{2}{3}[/tex]
We know that the slope-intercept of the line equation is
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
substituting (21, 78) and m = 2/3 in the slope-intercept of the line
[tex]y = mx+b[/tex]
[tex]78=\frac{2}{3}\left(21\right)+b[/tex]
switch sides
[tex]\frac{2}{3}\left(21\right)+b=78[/tex]
[tex]14+b=78[/tex]
[tex]b=64[/tex]
substituting b = 64 and m = 2/3 in the slope-intercept of the line
[tex]y = mx+b[/tex]
[tex]y\:=\:\frac{2}{3}x+64[/tex]
Therefore, the linear equation in the slope-intercept form will be:
[tex]y\:=\:\frac{2}{3}x+64[/tex]
