Question

point (0,5). 30. what is the equation of a line that is perpendicular to the line y = -¾ x - 2 and passes through the point (3,9). y = ⁴⁄₃ x + 5

Explanation:

Step1: Find perpendicular slope

The slope of $y = -\frac{3}{4}x - 2$ is $m_1 = -\frac{3}{4}$. The slope of a perpendicular line is the negative reciprocal: $m_2 = \frac{4}{3}$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m=\frac{4}{3}$, $x_1=3$, $y_1=9$:
$y - 9 = \frac{4}{3}(x - 3)$

Step3: Simplify to slope-intercept form

Expand and isolate $y$:
$y - 9 = \frac{4}{3}x - 4$
$y = \frac{4}{3}x - 4 + 9$
$y = \frac{4}{3}x + 5$

Answer:

$y = \frac{4}{3}x + 5$