Question

1. find the equation of each line described below.

a) perpendicular to ( y = \frac{1}{5}x - 2 ) but goes through ( (5, 25) )
b)

Explanation:

Step1: Identify slope of given line

The given line is $y = \frac{1}{5}x - 2$, so its slope $m_1 = \frac{1}{5}$.

Step2: Calculate perpendicular slope

Perpendicular slopes multiply to $-1$, so $m_2 = -\frac{1}{m_1} = -5$.

Step3: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m=-5$, $(x_1,y_1)=(5,25)$:
$y - 25 = -5(x - 5)$

Step4: Simplify to slope-intercept form

Expand and rearrange:
$y - 25 = -5x + 25$
$y = -5x + 50$

Answer:

$y = -5x + 50$