Perpendicular to the line y=1/2x-8; passes through (7,-6). Write the slope-intercept form of the equation.

ANSWER: The slope intercept form of the required line is y = -2x + 20. SOLUTION: Given, line equation is [tex]$y=\frac{1}{2} x-8$[/tex]And, Perpendicular line to the given line  passes through (7,-6).  We need to find the slope intercept form of perpendicular line of given line.  We already have the point (7, -6) but we need to find the slope. Now, we know that, product of slopes of two perpendicular lines equals to -1. Slope of given line is [tex]\frac{1}{2}[/tex], by comparing with the general form of slope intercept form. [tex]\frac{1}{2} \times[/tex] slope of required line = -1 Slope of perpendicular line = -2 Now, line equation of perpendicular line in point slope form is [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]y – (-6) = -2(x – 7) y + 6 = -2x + 14 y = -2x + 20 the above equation is in the form of slope intercept form of a line equation  where slope m = -2 and intercept c = 20 hence, the slope intercept form of the required line is y = -2x + 20.