Question

the equation of line v is $y = x + \frac{1}{7}$. parallel to line v is line w, which passes through the point $(-1, -2)$. what is the equation of line w?
write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Explanation:

Step1: Determine the slope of line w

Parallel lines have the same slope. The equation of line \( v \) is \( y = x+\frac{1}{7} \), which is in slope - intercept form \( y=mx + b \) (where \( m \) is the slope and \( b \) is the y - intercept). So the slope \( m \) of line \( v \) is 1. Therefore, the slope of line \( w \), which is parallel to line \( v \), is also 1.

Step2: Use the point - slope form to find the equation of line \( w \)

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1) \) is a point on the line and \( m \) is the slope. We know that \( m = 1 \) and the point \( (-1,-2) \) lies on line \( w \), so \( x_1=-1 \) and \( y_1 = - 2 \).
Substitute these values into the point - slope form:
\( y-(-2)=1\times(x - (-1)) \)
Simplify the left - hand side and the right - hand side:
\( y + 2=x + 1 \)

Step3: Convert to slope - intercept form

Subtract 2 from both sides of the equation \( y + 2=x + 1 \) to solve for \( y \):
\( y=x+1 - 2 \)
\( y=x - 1 \)

Answer:

\( y = x-1 \)