it is parallel, which means that the new line should have the same slope of the given line [tex] y=-5/4 x+7[/tex] 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 [tex]slope= \frac{y-y1}{x-x1} [/tex] where (x1,y1) is the point by which the new line passes through
[tex] \frac{-5}{4}=\frac{y-(-4)}{x-1}[/tex] [tex]\frac{-5}{4}= \frac{y+4}{x-1}[/tex] -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= [tex] \frac{-5}{4}x - \frac{11}{4}[/tex]
