Given:
The set of data points on the graph.
To find:
The equation of line that connects the set of data points.
Solution:
From the given graph it is clear that the data points are (20,40), (35,50), (50,60), (65,70).
If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Let as consider the line passes through (20,40) and (50,60), then the equation of line is
[tex]y-40=\dfrac{60-40}{50-20}(x-20)[/tex]
[tex]y-40=\dfrac{20}{30}(x-20)[/tex]
[tex]y-40=\dfrac{2}{3}(x-20)[/tex]
Multiply both sides by 3.
[tex]3(y-40)=2(x-20)[/tex]
[tex]3y-120=2x-40[/tex]
Isolate variable terms.
[tex]-2x+3y=120-40[/tex]
[tex]-2x+3y=80[/tex]
Therefore, the standard form of the required line is [tex]-2x+3y=80[/tex].
