Question

Write the equation, in standard form, of the line parallel to 4x− 7y = 7 that passes through (2, 9)

Answer 1

A parallel line will have the same slope.

So we need to find the slope of 4x - 7y = 7. We will put this equation in y = mx + b form, where m is the slope.
4x - 7y = 7
-7y = -4x + 7
y = -4x/-7 + 7/-7
y = 4/7x - 1
the number in the m position, 4/7, is the slope.

now we will use y = mx + b with slope(m) = 4/7 and points (2,9)
y = mx + b
9 = 4/7(2) + b
9 = 8/7 + b
9 - 8/7 = b
63/7 - 8/7 = b
55/7 = b
so your parallel equation is : y = 4/7x + 55/7 but we need it in standard form.
Ax + By = C
y = 4/7x + 55/7 -- multiply entire equation by 7
7y = 4x + 55 -- subtract 4x
-4x + 7y = 55 -- multiply by -1 to make x positive
4x - 7y = -55 ===> standard form

Answer 2

Thanks so much.

Answer 3

no problem :)