Question

find the equation of the line perpendicular to y=5x-1 that passes through the point (2,3).
○ y=5x+3
○ y=-(1)/(5)x+(17)/(5)
○ y=-5x+13
○ y=-(1)/(5)x+3

Explanation:

Step1: Identify slope of given line

The given line is $y=5x-1$, so its slope $m_1=5$.

Step2: Find perpendicular slope

Perpendicular slopes are negative reciprocals: $m_2 = -\frac{1}{m_1} = -\frac{1}{5}$

Step3: Use point-slope form

Point-slope formula: $y - y_1 = m_2(x - x_1)$, where $(x_1,y_1)=(2,3)$
$y - 3 = -\frac{1}{5}(x - 2)$

Step4: Simplify to slope-intercept form

Expand and isolate $y$:
$y = -\frac{1}{5}x + \frac{2}{5} + 3$
$y = -\frac{1}{5}x + \frac{2}{5} + \frac{15}{5}$
$y = -\frac{1}{5}x + \frac{17}{5}$

Answer:

y=-(1)/(5)x+(17)/(5)