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=(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=-(1)/(m_2)`
`\begin{gathered} m_1=(1)/(8) \\ (1)/(8)=-(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`