find x and y intercept of a line through point (3,5)

Question

y-5=m(x-3)

So I got this:

y=mx+(5-3m)

y incercept is (5-3m) but I don't know how to find the x intercept. Could someone help?

Answer 1

y-5=m(x-3)

y=mx-3m+5
y=mx+(-3m+5) which is a straight line gradient m with a y intercept of (0,5-3m).

Going back to the original if y=0

0-5=m(x-3)

-5=mx-3m

-5+3m=mx
x=(3m-5)/m

so the x intercept is ((3m-5)/m,0)

But check my maths!