Question

line v has an equation of y = 8x + 2. line w is parallel to line v and passes through (-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 slope of line w

Parallel lines have equal slopes. Line \( v \) has equation \( y = 8x + 2 \), so slope \( m = 8 \). Thus, line \( w \) also has \( m = 8 \).

Step2: Use point - slope form

Point - slope form is \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(-1,-2) \) and \( m = 8 \). Substitute: \( y - (-2)=8(x - (-1)) \), which simplifies to \( y + 2 = 8(x + 1) \).

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y + 2 = 8x+8 \). Subtract 2 from both sides: \( y = 8x + 8 - 2 \), so \( y = 8x+6 \).

Answer:

\( y = 8x + 6 \)