Question

Find the equation of the line that is perpendicular to y = – 1 4 x – 8 and passes though the point (2, –4).

Answer 1

The equation of the line is $y=\frac{1}{4}x-\frac{29}{7}$

Explanation:

The equation of the line is perpendicular to $y=-14 x-8$

The equation is of the form $y=mx+b$ where m=-14

Slope:

The slope of the perpendicular line can be determined using the formula,

$m_1 \cdot m_2=-1$

$-14 \cdot m_2=-1$

       $m_2=\frac{1}{14}$

Thus, the slope of the line is $m=\frac{1}{14}$

Equation of the line:

The equation of the line can be determined using the formula,

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

Substituting the slope $m=\frac{1}{14}$ and the point (2,-4), we get,

$y+4=\frac{1}{14}(x-2)$

Simplifying, we get,

$y+4=\frac{1}{14}x-\frac{1}{7}$

     $y=\frac{1}{14}x-\frac{1}{7}-4$

     $y=\frac{1}{4}x-\frac{29}{7}$

Thus, the equation of the line is $y=\frac{1}{4}x-\frac{29}{7}$