Question

write an equation of the line that passes through (-1,-7) and its perpendicular to the line y=1/5x-2

Answer 1

Formula for a line with slope \(m\) passing through point \((x_0,y_0)\) is \[y-y_0=m(x-x_0)\]

The line \(y =\frac{1}{5}x-2\) is in slope-intercept form, \(y=mx+b\) so we know its slope. The product of the slopes of perpendicular lines is -1, so if we take
\[m=\frac{-1}{\frac{1}{5}}\]we have the slope of our new line. Then just plug in the known point and that slope and you've got your equation.