The straight line l1 has gradient m and has x intercept 6.
a) Show clearly that the equation of l1 can be written as y +mx = 6.
The straight line l2, with equation y =2x +9 , meets l1 at the point A .
b) Determine the coordinates of A
for a gradient or slope of m
and x-intercept of 6, which would be the point (6,0)
the equation would be
y-0 = m(x-6)
y = mx - 6m
mx - y = 6m would be the equation, which is not the same as
y + mx = 6
if L1 intersects y = 2x + 9 at A,
mx - 6m = 2x + 9
mx - 2x = 9 + 6m
x(m-2) = 9+6m
x = (9+6m)/(m-2) , but y = mx - 6m
then y = m(9+6m)/(m-2) - 6m
= (9m + 6m^2 - 6m + 12)/(m-2)
= (6m^2 + 3m + 12)/(m-2)
check my algebra