Question

Find the equation of the line through (−8,1) which is perpendicular to the line y=−x/2−6.
Give your answer in the form y=mx+b.

Answer 1

Linear equations can represent parallel lines, perpendicular lines and lines with no relationship at all.

The equation of the line in form of y =mx + b is $\mathbf{y = 2x + 17}$

The equation is given as:

$\mathbf{y =-\frac x2 - 6}$

For a linear equation y = mx + b, the slope of the equation is m

So, by comparison:

$\mathbf{m =-\frac 12}$

The relationship between the slopes of perpendicular lines is:

$\mathbf{m_2 =-\frac 1{m_1}}$

So, we have:

$\mathbf{m_2 =-\frac 1{-1/2}}$

$\mathbf{m_2 =2 }$

This means that, the slope of the line that passes through point (-8,1) is 2

The line equation is then calculated as:

$\mathbf{y = m(x - x_1) + y_1}$

This gives

$\mathbf{y = 2(x + 8) + 1}$

Open brackets

$\mathbf{y = 2x + 16 + 1}$

Simplify

$\mathbf{y = 2x + 17}$

Hence, the equation of the line in form of y =mx + b is $\mathbf{y = 2x + 17}$

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