Question

Line p is represented by the equation 2x-y=-5 . if line r passes through point (6,4), and is perpendicular to line p, what is the equation of line r

Answer 1

Given that Line p is represented by the equation;

`2x-y=-5`

Re-writing the equation in the slope intercept form, we have;

`y=2x+5`

Also, line r passes through point (6,4), and is perpendicular to line p;

The slope of line r can be calculated using the formula for perpendicular lines;

`m_p* m_r=-1`

The product of the slope of two perpendicular lines equals -1.

`\begin{gathered} m_r=(-1)/(m_p) \\ m_p=2 \\ m_r==(-1)/(2) \end{gathered}`

Finally, since we have the slope of line r, let us apply the point slope equation of a line to get the equation of line r;

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

Given the point;

`\begin{gathered} (x_1,y_1)=(6,4) \\ m_r=(-1)/(2) \end{gathered}`

So, subtituting this values, we have;