Question

find the equation of the line perpendicular to $y = -\frac{3}{4}x + 8$, that passes through $(-9, -2)$. is the slope of this line positive or negative? a) positive b) negative

Explanation:

Step1: Find perpendicular slope

The slope of the given line is $m_1 = -\frac{3}{4}$. Perpendicular slopes multiply to $-1$, so $m_2 = \frac{4}{3}$.

Step2: Confirm slope sign

$\frac{4}{3} > 0$, so the slope is positive.

Step3: Verify (optional)

Using point-slope form $y - y_1 = m_2(x-x_1)$ confirms the slope remains positive.

Answer:

a) positive