Question

3 which line is perpendicular to the given line and passes through the point (-8, 3)? given: $y + 5 = -4(x - 2)$ a $y = 4x + 3$ b $y = \frac{1}{4}x + 5$ c $y = -\frac{1}{4}x + 1$ d $y = \frac{1}{4}x - 5$

Explanation:

Step1: Find slope of given line

The given line is \( y + 5 = -4(x - 2) \), which is in point - slope form \( y - y_1=m(x - x_1) \), so its slope \( m_1=-4 \).

Step2: Find slope of perpendicular line

For two perpendicular lines, the product of their slopes is \( - 1 \). Let the slope of the perpendicular line be \( m_2 \). Then \( m_1\times m_2=-1 \), so \( - 4\times m_2=-1 \), which gives \( m_2=\frac{1}{4} \).

Step3: Use point - slope form to find equation

We know the line passes through \( (-8,3) \) and has slope \( \frac{1}{4} \). The point - slope form is \( y - y_1=m(x - x_1) \), substituting \( x_1=-8,y_1 = 3,m=\frac{1}{4} \), we get \( y - 3=\frac{1}{4}(x + 8) \).
Simplify this equation: \( y-3=\frac{1}{4}x + 2 \), then \( y=\frac{1}{4}x+5 \).

Answer:

B. \( y=\frac{1}{4}x + 5 \)