Can someone me understand i dont know what to even do. write an equation for the line parallel to the given line that contains c. c(4,7); y= -4x+5

Remember that a parallel line has the same slope...
So we already know the slope of the line containing point C is -4.

Using point slope equation, we can do...

y-y₁=m(x-x₁)
y-7= -4(x-4)
y-7- -4x+16
*Add seven to both sides...* y=-4x+23

There is you answer... hope this helps!

If a line is parallel to another line, both lines have the same slope. The slope of the line is -4, which means the slope of the parallel line would be -4.
Parallel lines never intersect, which means the y-intercept of the parallel line cannot be 5. The y-intercept of the parallel line is when x = 0. You know that one of the points of the new, parallel line is (4,7). So what happens if you use the slope to find the y-intercept? So you can take the point (4,7) and subtract 4 from the x-coordinate and add 16 to the y-coordinate (Remember, this is the slope because the change in y is 16, and the change in x is -4, making the slope -4). When you do this, then you get that the y-intercept is 23. Therefore, the equation for the line is y = -4x + 23.

The answer for you question is b