How do you write the equation of this line and this point in standard form?

There are two ways to write equation

1) Ax + By +C =0 Where A, B and C are numbers

2) y = m x + C where m is slope of the line with x-axis and C is intersection on y- axis.

The question is not clear to me. I do not understand what is (through (-3/4, -1/7)

The line described by the equation given does not pass through that point.

Your equation can be write as

4 x - 15 y -6 = 0 where A=4, B=-15 and C=-6

Other way we can write as y = 4/15 x - 6/15 where m = 4/15 and C = -6/15

You left out a key word: is it parallel to or perpendicular to? I'll guess parallel (50-50 chance)

That means it has the same slope, and therefore the same x and y parts, so it

starts as 2/3 x - 5/2 y = ....

Plug in -3/4 for x and -1/7 for y to see how it ends.

2/3 (-3/4) - 5/2 (-1/7)

-1/2 + 5/14

-7/14 + 5/14

-2/14 = -1/7

so 2/3 x - 5/2 y = -1/7

Now get rid of the fractions since standard form only uses integers by multiplying by the LCD, 42

28x - 105y = -6