Question

Could someone please help me write an equation of the line containing the given point and parallel to the given line.
(6,-9)4x-5y=8
Y=?

Answer 1

Note that when two lines are parallel, their slopes are equal. The given equation is 4x - 5y = 8. To get its slope, we change it to the form
y = mx + b
where m is the slope and b is the y-intercept. Therefore,
4x - 5y = 8
-5y = -4x + 8
y = (4/5)x - 8/5

The slope is equal to 4/5. Thus the slope of the line passing through the point (6, -9) is also 4/5.
Now to get the equation of line, recall that given a slope and a point on the line, we the point-slope form:
y - y1 = m(x - x1)
where (x1, y1) is the point. Substituting,
y - (-9) = (4/5)(x - 6)
y + 9 = (4/5)x - 24/5
y = (4/5)x - 24/5 - 9 ; note that 9 is also 45/5
y = (4/5)x - 69/5

Hope this helps~ :3

Answer 2

easiest way:

As Jai pointed out , the two lines are parallel so their equations must differ only in the constant

let the new equation be 4x - 5y = c
but (6,-9) lies on it, so
24 + 45 = c = 69

new equation: 4x - 5y = 69

which can be easily changed to
y = (4/5)x - 69/5 if need be.