Question

Find the equation of a line that goes through the point ( 1,- 6 ) and is perpendicular to the line: y = (1 / 8)x - 9

Answer 1

Step 1

Given;

$\begin{gathered} y=\frac{1}{8}x-9 \\ with\text{ points \lparen1,-6\rparen} \end{gathered}$

Required; Find the equation of a line that goes through the point ( 1,- 6 ) and is perpendicular to the line: y = (1 / 8)x - 9

Step 2

For perpendicular lines, the relationship between the slopes is;

$m_1=-\frac{1}{m_2}$$\begin{gathered} m_1=\frac{1}{8} \\ \frac{1}{8}=-\frac{1}{m_2} \\ m_2=-8 \end{gathered}$

The y-intercept is found thus;

$\begin{gathered} y=-8x+b \\ b=y-intercept \\ y=-6 \\ x=1 \\ -6=-8(1)+b \\ b=-6+8=2 \end{gathered}$

Answer; The required equation will be;

$y=-8x+2$