Question

Write the standard form of the line that is parallel to
2x + 3y = 4 and passes through the point (1, -4)

Answer 1

2x + 3y = 4 is already in "standard form of the equation of a straight line."
So the new equation will look the same, EXCEPT that the constant will no longer be 4.

Think: 2x + 3y = c
Substitute the x- and y-coordinates of the given point into 2x + 3y = c; find c.

Then write out the "standard form of the equation of a straight line" with your c substituted.

Answer 2

if you use the form y=mx+b, then you will want to convert 2x+3y=4, into the format y=mx+b

so make y the subject

2x+3y=4
3y=-2x+4


a line that is parallel to this, will have the same gradient. This is the only rule you need to know so using the form
y=mx+b
m is the slope, our slope is -2/3
and b is any constant translation
so

hence, this line is parallel to the one you currently have, so to choose a specific line parallel, you can put any value of b that you want, whether b=2,3,5,6,7,8
but it can not be the same number that you had originally, which is 4

so
would work