Question

question 15 a line passes through the point (0,2) and is perpendicular to the line $y=-(1)/(4)x + 5$. what is its equation? $\bigcirc$ $y=(1)/(4)x + 2$ $\bigcirc$ $y=-(1)/(4)x + 2$ $\bigcirc$ $y = 4x + 2$ $\bigcirc$ $y=-4x + 2$

Explanation:

Step1: Identify given line's slope

The given line is $y=-\frac{1}{4}x+5$, so its slope $m_1=-\frac{1}{4}$.

Step2: Find perpendicular slope

Perpendicular slopes multiply to -1. Let new slope be $m_2$.
$$m_2 = \frac{-1}{m_1} = \frac{-1}{-\frac{1}{4}} = 4$$

Step3: Use point to find y-intercept

The line passes through $(0,2)$, which is the y-intercept ($b=2$).

Step4: Write line equation

Use slope-intercept form $y=mx+b$.

Answer:

C. $y=4x+2$