Question

1. what is the equation of a line passing through (2, -1) and parallel to the line represented by the equation $y = 2x + 1$?
2. $y = -\frac{1}{2}x$
3. $y = -\frac{1}{2}x + 1$
4. $y = 2x - 5$
5. $y = 2x - 1$

Explanation:

Step1: Determine the slope of the parallel line

Parallel lines have the same slope. The given line is \( y = 2x + 1 \), which is in slope - intercept form \( y=mx + b \) where \( m \) is the slope. So the slope \( m \) of the line we want to find is also \( 2 \).

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

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(2,-1) \) and \( m = 2 \).
Substitute the values into the formula:
\( y-(-1)=2(x - 2) \)
Simplify the left - hand side: \( y + 1=2(x - 2) \)
Expand the right - hand side: \( y+1 = 2x-4 \)
Subtract 1 from both sides to get the slope - intercept form: \( y=2x-4 - 1=2x - 5 \)

Answer:

1. \( y = 2x-5 \)