Question

lines m and n are parallel. line m is described by the equation $y = 4x + 2$. line n contains the point $(1, -3)$. which of the following is an equation for line n?
a. $y - 3 = 4(x + 1)$
b. $y - 3 = -\frac{1}{4}(x + 1)$
c. $y + 3 = 4(x - 1)$
d. $y + 3 = -\frac{1}{4}(x - 1)$

Explanation:

Step1: Determine the slope of line \(n\)

Since lines \(m\) and \(n\) are parallel, and the equation of line \(m\) is \(y = 4x+2\) (in the form \(y=mx + b\) where \(m\) is the slope), the slope of line \(n\) is also \(m = 4\).

Step2: Use the point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(1,-3)\) and \(m = 4\).
Substitute the values into the formula: \(y-(-3)=4(x - 1)\), which simplifies to \(y + 3=4(x - 1)\)

Answer:

C. \(y + 3=4(x - 1)\)