Question

find the equation of the line perpendicular to $y = -\frac{7}{4}x - 5$, that passes through (7, 6).
is the slope of this line positive or negative?
a) positive b) negative

Explanation:

Step1: Find perpendicular slope

Perpendicular slopes are negative reciprocals. Original slope is $m_1 = -\frac{7}{4}$, so new slope is $m_2 = \frac{4}{7}$.

Step2: Solve for intercept

Use point-slope form $y - y_1 = m(x-x_1)$ with $(7,6)$:
$y -6 = \frac{4}{7}(x-7)$
Simplify to slope-intercept form:
$y = \frac{4}{7}x -4 +6 = \frac{4}{7}x +2$

Step3: Classify slope sign

$\frac{4}{7} > 0$, so slope is positive.

Answer:

a) positive
The equation of the line is $y=\frac{4}{7}x +2$.