Question

how do you find the value of x or y so that the line through the points has a given slope?

Answer 1

     We can make a linear equation system to deduce it.

$\left \{ {{y_1=ax_1+b~(I)} \atop {y_2=ax_2+b~(II)}} \right. \\ \\ (II)-(I): y_2-y_1=a(x_2-x_1) \\ \\ \boxed {a= \frac{\Delta x}{\Delta y} }$

Answer 2

ok so if you had the points
(x1,y1) and (x2,y2)
slope=rise/run so
slope=(y2-y1)/(x2-x1)