Generate $x$ values using start and end points using Slope equation/formula

Question

I know the start and the end points of a slope.How do I get all the $(x,y)$ values between the start and end point. For example: When $x = 0$, $y = 5$ and $x = 20000$, $y = 20$. How do I generate the $y$ values when $x$ ranges from $0$ to $20000$?

Answer 1

Slope formula:

$$m=\frac{y_2-y_1}{x_2-x_1}=\frac{20-5}{20000-0}=\frac3{4000}$$

Point-slope formula:

$$y-y_2=m(x-x_2)$$

$$y-5=\frac3{4000}(x-0)=\frac3{4000}x$$

$$y=\frac3{4000}x+5$$

Answer 2

The points satisfy an equation $y=ax+b$, the equation of a (non-vertical) line. You need to find out the values of $a$ and $b$. If you plug in the points you already have, you get the system

$$\left\{\begin{array}{l} 5=a\cdot0+b\\ 20=a\cdot20000+b \end{array}\right.$$

Do you think you can take it from here?