Question

Write an equation of a line that is perpendicular to y=3x+5 and contains the point (0,0).

Answer 1

To write the equation of a line you need to identify the slope (m) and the y-intercept (b):

$y=mx+b$

Slope:

Perpendicular lines have slopes that are opposite of the reciprocal of each other.

As the given line is perpendicular to y=3x+5 (slope m=3) the slope is:

$\begin{gathered} \text{slope}=m \\ \\ Perpendicular\text{ slope = -}\frac{1}{m} \\ \\ Perpendicular\text{ slope = }-\frac{1}{3} \end{gathered}$

Y-intercept:

Value of the line (y coordinate) when it cross the y-axis (when x is equal to 0)

As the given line contains the point (0,0) the value of y when x is 0 is also 0

y.intercept=0

Then, you get the next equation for the line:

$y=-\frac{1}{3}x$