find slope intercept of the equation of the line parallel to?

Parallel means same slope,
-4=-4/7(21)+b,
-4=-12+b,
b=-4-(-12)=8,
y=-4/7x+8.
Answer: y=-4/7x+8.

Any line can be written in the form

y = mx + b

Where m is the slope and b is the y-intercept.

When two lines are parallel, they have the same slope. So you know that the slope of your desired line is also -4/7.

y = (-4/7)x + b

We need to solve for b. Fortunately, we are given an (x,y) that we know is on the line.

-4 = (-4/7)(21) + b
-4 = -12 + b
8 = b

So in general terms, the equation of the line is
y = (-4/7)x + 8

y - y1 = m(x - x1 )
where m is the slope and ( x1, y1 ) is any point on the line.

y + 4 = ( - 4 / 7 )(x - 21 )
y + 4 = ( - 4 / 7 )x + 12
y = ( - 4 / 7 )x + 8

The line you're looking for also has slope -4/7. Substitute into y=mx+b to get:
-4 = (-4/7)(21) + b
-4 = -12 + b
8 = b
So, the equation of the line is
y = (-4/7)x + 8