Question

line lh is perpendicular to line za. line za is represented by the equation y = -\frac{1}{2}x - \frac{25}{2}. line lh passes through the point l (8, 10). determine the equation of line lh in slope - intercept form.
slope of line za | slope of line lh | point - slope form of line lh
m1 | m2 | y - y1 = m(x - x1)
-\frac{1}{2} | 2 | y - 10 = 2(x - 8)

Explanation:

Step1: Find the slope of line LH

Perpendicular lines have slopes that are negative - reciprocals. Given the slope of line ZA $m_1 =-\frac{1}{2}$, the slope of line LH $m_2 = 2$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. We know $m = 2$ and the point $(x_1,y_1)=(8,10)$, so $y - 10=2(x - 8)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y-10 = 2x-16$. Then add 10 to both sides: $y=2x - 6$.

Answer:

$y = 2x-6$