Question

give the equation of a line that goes through the point (15,6) and is perpendicular to the line 5x + 9y = -27. give your answer in slope intercept form question help: video message instructor submit question

Explanation:

Step1: Find slope of given line

Rewrite $5x + 9y = -27$ to slope-intercept form $y=mx+b$:
$9y = -5x -27$
$y = -\frac{5}{9}x - 3$
Slope of given line: $m_1 = -\frac{5}{9}$

Step2: Find perpendicular slope

Perpendicular slope $m_2$ is negative reciprocal:
$m_2 = \frac{9}{5}$

Step3: Use point-slope form

Use point $(15,6)$ and $m_2=\frac{9}{5}$ in $y - y_1 = m(x - x_1)$:
$y - 6 = \frac{9}{5}(x - 15)$

Step4: Convert to slope-intercept form

Simplify the equation:
$y - 6 = \frac{9}{5}x - 27$
$y = \frac{9}{5}x - 27 + 6$
$y = \frac{9}{5}x - 21$

Answer:

$y = \frac{9}{5}x - 21$