Question

Write an equation of the line containing the given point and parellel to the given line.

(2,-6); 9x-5y=4

Answer 1

rearranging the given line,
y = (9/5)x - 4/5 (1)
which has the form
y = mx + b (2)
where m is the slope and b is the y intercept.
The new line would have the same slope to be parallel, so it would have the form:
y = (9/5)x + b (3)
to solve for b, input the given coordinates, obtaining:
(-6) = (9/5)(2) + b
rearrange and solve for b, then substitute back into equation (3)

Answer 2

It looks like b = -30/5 -18/5 = -48/5
So
y = (9/5)x - 48/5
(or 9x-5y=48)

Check: when x = 2,
y = 18/5 - 48/5 = -30/5 = -6
Looks OK

Answer 3

The new equation must be something like
9x - 5y = c
plug in the given point(2,-6)
18 + 30 = c = 48

all done : 9x - 5y = 48