How do you write the equation of a line with only the x-intercept and coordinates pair?

Answer 1

You can only do so if the coordinate pair is other than the x intercept.

Suppose the x intercept is A = (a, 0) and suppose the coordinate pair is R = (s, t)

Then gradient = (t-0)/(s-a) = t/(s-a)

Suppose P = (x, y) are the coordinates of any point on the line. Then gradient of PA = (y-0)/(x-a) = y/(x-a)

The two gradients must be the same so t/(s-a) = y/(x-a)

or y*(s-a) = t*(x-a)

or y = t/(s-a)*x - ta/(s-a) which is of the form y = mx + c

with m = t/(s-a)

and c = -ta(/(s-a)