Given
Points (5,190000), (10,210000) and (20,250000)
Solve for the slope of the line
To solve for the slope of the line, recall the formula
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are any two points in the graph} \end{gathered}[/tex]
For this case we will use (5,190000) and (10,210000)
[tex]\begin{gathered} (x_1,y_1)=\mleft(5,190000\mright) \\ (x_2,y_2)=\mleft(10,210000\mright) \\ \\ \text{Substitute to the slope formula} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{210000-190000}{10-5} \\ m=\frac{20000}{5} \\ m=4000 \end{gathered}[/tex]
Now that we have m = 4,000, we will use this to solve for the y-intercept.
Recall the slope-intercept form of a linear equation
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]
We will use point (10,210000), in this case
[tex]\begin{gathered} \text{Substitute the following} \\ (x,y)=\mleft(10,210000\mright) \\ m=4000 \\ \\ \text{THEN} \\ y=mx+b \\ 210000=40000+b \\ 210000=40000+b \\ 250000-40000=b \\ b=170000 \end{gathered}[/tex]
Summarizing everything, the equation of the line is
[tex]p=f(h)=4000h+170000[/tex]
