Question

Write an equation that passes through (4,-3) and is perpendicular to y=-2x-4

Answer 1

The point is (4,-3) and is perpendicular to y=-2x-4.

The slope is given , m=-2.

For the perpendicular line, the slope is

$m_1\times m_2=-1$$m_1\times-2=-1$$m_1=\frac{1}{2}$

Now, then the general equation is

$y-y_1=m(x-x_1)$

Substitute the values.

$y-(-3)=\frac{1}{2}(x-4)$$y+3=\frac{1}{2}(x-4)$$y=\frac{1}{2}x-\frac{4}{2}-3$$y=\frac{1}{2}x-2-3$$y=\frac{1}{2}x-5$

Hence the equation is determined as

$y=\frac{1}{2}x-5$