Question

Is it parallel or is it perpendicular?

Answer 1

It is parallel, which means that the new line should have the same slope of the given line $y=-5/4 x+7$
and the slope is the coefficient of x 
so the slope = -5/4
in order to solve this problem we have to know the equation of the slop
$slope= \frac{y-y1}{x-x1}$
where (x1,y1) is the point by which the new line passes through 

$\frac{-5}{4}=\frac{y-(-4)}{x-1}$
$\frac{-5}{4}= \frac{y+4}{x-1}$
-5(x-1)=4(y+4)
-5x +5=4y+16 (by subtracting 16 from both sides)
-5x -11= 4y (divide both sides by 4)
y= $\frac{-5}{4}x - \frac{11}{4}$