Find the equation of the line that contains the given point and is perpendicular to the given line . write the equation in slope intercept form. (4,1) y= -4x-7 show work

Ok, so a line with a perpendicular slope will have the opposite reciprocal slope, meaning that if the slope on y=-4x-7 is -4, the opposite reciprocal slope would be 1/4. so, if you plug the given point into your new line,

y=1/4x+b
1=1/4(4)+b
1=1+b
b=0

so, the final equation would be y=1/4x
(i think?)