Question

find an equation of the line l, where l is perpendicular to ( y = \frac{5}{3}x ) and passes through the point (3,5). ( y = ) (type your answer in slope - intercept form. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Find perpendicular slope

The slope of $y=\frac{5}{3}x$ is $\frac{5}{3}$. The slope of a perpendicular line is the negative reciprocal: $m=-\frac{3}{5}$.

Step2: Use point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$. Substitute $m=-\frac{3}{5}$, $x_1=3$, $y_1=5$:
$y-5=-\frac{3}{5}(x-3)$

Step3: Convert to slope-intercept form

Expand and solve for $y$:
$y-5=-\frac{3}{5}x+\frac{9}{5}$
$y=-\frac{3}{5}x+\frac{9}{5}+5$
$y=-\frac{3}{5}x+\frac{9}{5}+\frac{25}{5}$
$y=-\frac{3}{5}x+\frac{34}{5}$

Answer:

$y=-\frac{3}{5}x+\frac{34}{5}$