Given equation of line y=0.25x-7.
On comparing given equation with slope-intercept form y=mx+b.
We get m=0.25.
0.25 could be written 25/100 in simplest fractions 1/4.
Line are perpendicular.
Therefore, slope of the perpendiular line would be reciprocal and opposite in sign of the given slope of the line.
Reciprocal of 1/4 is 4 and opposite of sign of 4 would be -4.
So, the slope of the required line is m=-4.
We are given a point (-6,8).
Applying point-slope form, we get
y-y1=m(x-x1)
y-8 = -4(x- (-6))
y-8 = -4(x+6)
y-8 = -4x -24.
Adding 8 on both sides, we get
y-8=8 = -4x -24+8
y=-4x-16.
Therefore, the equation y=-4x-16 is perpendicular to the given eqution of line.
