Answer:
B. & E.
Step-by-step explanation:
First, to find your slope, put your line into slope-intercept form.
[tex]y=mx+b\\[/tex]
[tex]3x-4y=7\\-4y=-3x+7\\y=\frac{3}{4} x-\frac{7}{4}[/tex]
Your slope is [tex]\frac{3}{4}[/tex].
Now, you can find the y-intercept of your parallel line by plugging your given point and your slope into point-slope form.
[tex]y-y1=m(x-x1)\\y-(-2)=\frac{3}{4} (x-(-4))\\y+2=\frac{3}{4} (x+4)\\y+2=\frac{3}{4} x+3\\y=\frac{3}{4} x+1[/tex]
Your y-intercept is 1.
If you notice, answer choice E is equivalent to one of our steps in converting it to point-slope form. Therefore, E is one of your answers.
The equation of your parallel line is:
[tex]y=\frac{3}{4} x+1[/tex]
B is also a correct answer.
If you put B into slope-intercept form, you get the following:
[tex]3x-4y=-4\\-4y=-3x-4\\y=\frac{3}{4} x+1[/tex]
This, of course, is equivalent to the parallel line which we already found, so we know it is parallel.
