find the equation of the line in all 3 forms (standard, slope intercept & point slope)

Question

parallel to 3x-7y=4, through (3,-4)

Answer 1

Obviously, one purpose of this problem is to teach the three forms of the equation of a line that are mentioned. It is also important to know that parallel lines have the same slope,

The parallel line has the form 3x-7y=D [note: convert to slope-intercept form and back]

3(3) -7(-4) = D [note that this is Ax+By=C and slope is -A/B = 3/7]

37 = D

The equation of the parallel line is:

3x - 7y = 37 [Standard form is Ax+By=C]

y = (3/7)x -37/7 [Slope-intercept form is y = mx + b]

(y + 4) = (3/7)(x - 3) [Point-slope form is (x-x1) = m(y-y1) ]

Answer 2

3/7= (y+4)/(x-3) is the equation you need.

You should be able to "massage" it into the forms needed. If not, make a comment and I will try to help further.