write the equation of a line that is perpendicular to $y = 0.25x - 7$ and that passes through the point…

Explanation:

Step1: Find the slope of the perpendicular line

The slope of the given line ( y = 0.25x - 7 ) is ( m_1 = 0.25=\frac{1}{4} ). For two perpendicular lines, the product of their slopes is ( - 1 ), so the slope ( m_2 ) of the perpendicular line satisfies ( m_1\times m_2=-1 ). Substituting ( m_1=\frac{1}{4} ), we get ( \frac{1}{4}\times m_2=-1 ), then ( m_2=-4 ).

Step2: Use point - slope form to find the equation

The point - slope form of a line is ( y - y_1=m(x - x_1) ), where ( (x_1,y_1)=(-6,8) ) and ( m = - 4 ). Substituting these values into the formula: ( y - 8=-4(x + 6) )

Step3: Simplify the equation to slope - intercept form

Expand the right - hand side: ( y - 8=-4x-24 ) Add 8 to both sides: ( y=-4x-24 + 8=-4x-16 )

Answer:

The equation of the line is ( y=-4x - 16 )