Question

line bn is represented by the equation $y = \frac{3}{4}x + \frac{7}{4}$. determine the equation, in slope - intercept form, of the line hz that is perpendicular to line bn and passes through the point $h(-6, 7)$.
$y = \square$
(there is a coordinate grid with points b, h, n plotted. also, a table with columns: slope of line bn, slope of line hz, point - slope form of line hz)

Explanation:

Step1: Find slope of BN

Line BN: \( y = \frac{3}{4}x + \frac{7}{4} \), so \( m_1 = \frac{3}{4} \).

Step2: Find slope of HZ (perpendicular)

Perpendicular slopes: \( m_1 \cdot m_2 = -1 \), so \( m_2 = -\frac{4}{3} \).

Step3: Use point - slope form

Point \( H(-6, 7) \), point - slope: \( y - 7 = -\frac{4}{3}(x + 6) \).

Step4: Convert to slope - intercept

Expand: \( y - 7 = -\frac{4}{3}x - 8 \).
Add 7: \( y = -\frac{4}{3}x - 1 \).

Answer:

\( y = -\frac{4}{3}x - 1 \)