Question

Write the equation of a line PERPENDICULAR to y = -1/3x + 5 and passes through
the point (6,4)

Answer 1

Answer:

$y = 3\, x - 14$.

Step-by-step explanation:

The slope-intercept form equation of a slanting line is in the form $y = m\, x + b$, where $m$ would be the slope of that line.

The equation of the original line is given in the slope-intercept form: $y = (-1/3)\, x + 5$. The slope of that line would thus be $(-1/3)$.

Two slanted lines in a plane are perpendicular to one another if and only if their slopes are inverse reciprocals.

In other words, if the slope of two slanted lines are $m_{1}$ and $m_{2}$, those two lines would be perpendicular to one another if and only if $m_{1} \cdot m_{2} = (-1)$.

In this question, the slope of the given line is $m_{1} = (-1/3)$. Rearrange the equation $m_{1} \cdot m_{2} = (-1)$ to find $m_{2}$, the slope of the line perpendicular to the given line:

$\begin{aligned}m_{2} &= \frac{-1}{m_{1}} \\ &=\frac{-1}{-1/3} \\ &= 3\end{aligned}$.

In other words, the slope of the line perpendicular to the given line would be $3$.

If a line of slope $m$ goes through the point $(x_{0},\, y_{0})$, the point-slope equation of that line would be $y - y_{0} = m\, (x - x_{0})$.

In this question, the requested line goes through the point $(6,\, 4)$. It was also deduced that the slope of this requested line is be $3$. The equation of this line in point-intercept form would be:

$y - 4 = 3\, (x - 6)$.

Rearrange to find the equation of this line in slope-intercept form:

$y = 3\, x - 14$.