Question

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) Write the equation of the line x 3y

Answer 1

Answer:

$y = -3x + 14$

Step-by-step explanation:

Required

The equation of line

perpendicular to : $x -3y =9$

Passes through $(3,5)$

We have:

$x -3y =9$

Make y the subject

$3y =x - 9$

Solve for y

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

Compare the above equation to $y = mx + c$

$m =\frac{1}{3}$ ---- This represents the slope

Since the line is perpendicular to $x -3y =9$, then its slope is:

$m_2 = -\frac{1}{m}$

$m_2 = -\frac{1}{1/3}$

$m_2 =-3$

The equation of the perpendicular line is:

$y =m_2(x - x_1) + y_1$

Where:

$m_2 =-3$

$(x_1,y_1) =$ $(3,5)$

So:

$y = -3(x - 3) + 5$

$y = -3x + 9 + 5$

$y = -3x + 14$