Question

What is the equation of a line in slope intercept form that is perpendicular to the line y=2x+7 and passes through the point (-2,4)

Answer 1

It is given that the line is perpendicular to the line y=2x+7.

Slope of given line=2.

Let the slope of required line be m.

Since the required line is perpendicular to the given line, so it follows:

$m=-\frac{1}{2}$

Since the product of slopes of perpendicular lines is -1.

It is also given that the line passes through (-2,4) so by slope-point form, the equation is given by:

$\begin{gathered} y-4=-\frac{1}{2}(x-(-2)) \\ 2y-8=-(x+2) \\ 2y-8=-x-2 \\ x+2y-6=0 \end{gathered}$

So the equation is x+2y-6=0.