Question

the equation of line p is y = -4x + 1. line q is perpendicular to line p and passes through (-6, 1). what is the equation of line q? write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Explanation:

Step1: Find the slope of line q

The slope of line \( p \) is \( -4 \). For two perpendicular lines, the product of their slopes is \( -1 \). Let the slope of line \( q \) be \( m \). Then \( -4 \times m = -1 \), so \( m = \frac{1}{4} \).

Step2: Use point - slope form to find the equation of line q

The point - slope form of a line is \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(-6,1) \) and \( m=\frac{1}{4} \).
Substitute the values into the formula: \( y - 1=\frac{1}{4}(x + 6) \)

Step3: Convert to slope - intercept form (\( y=mx + b \))

Expand the right - hand side: \( y - 1=\frac{1}{4}x+\frac{6}{4}=\frac{1}{4}x+\frac{3}{2} \)
Add 1 to both sides: \( y=\frac{1}{4}x+\frac{3}{2}+1=\frac{1}{4}x+\frac{3 + 2}{2}=\frac{1}{4}x+\frac{5}{2} \)

Answer:

\( y=\frac{1}{4}x+\frac{5}{2} \)