Write the equation of a line that is perpendicular to y=0.25x-7y=0.25x−7y, equals, 0, point, 25, x, minus, 7 and that passes through the point (-6,8)(−6,8)left parenthesis, minus, 6, comma, 8, right parenthesis.

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.