how to make an line more tall and still on the same lope?

Question

H how i can make an line more tall Provided that tall on the same slope i have image explain what i need.

please See this image

    so how i can find the next x2 ,y2 for the red or the secend  line
    or the point to of secend line

and how i can to make this tall specfic example i want to Increase line by 6

thanks every one

Answer 1

First you should find the slope of the original segment. Let $m$ represent the slope of the segment. $$m=\frac{y_2-y_1}{x_2-x_1}$$

Then, however much you extend $x$ by, extend $y$ by $m*x$

For example, you could make a new endpoint at $(x_2+4,y_2+m*4)$

Full example: if your points are $(1,1)$ and $(3,4)$ then the slope is $m=\frac{4-1}{3-1}=\frac{3}{2}$

So, you could then extend the line from $(3,4)$ to, for example, $(3+10, 4+\frac{3}{2}*10)$ or $(13,19)$