Question

the equation for line u can be written as y = -2x + 10. line v, which is parallel to line u, includes the point (-1, 2). what is the equation of line v?
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 v

Parallel lines have equal slopes. Line \( u \) has equation \( y = -2x + 10 \), so slope \( m = -2 \). Thus, line \( v \) also has \( m = -2 \).

Step2: Use point - slope form

Point - slope form is \( y - y_1 = m(x - x_1) \). Line \( v \) passes through \( (-1, 2) \), so \( x_1=-1 \), \( y_1 = 2 \), \( m=-2 \). Substitute: \( y - 2=-2(x - (-1)) \), which simplifies to \( y - 2=-2(x + 1) \).

Step3: Convert to slope - intercept form

Expand \( y - 2=-2x-2 \). Add 2 to both sides: \( y=-2x - 2 + 2 \), so \( y=-2x+0 \) (or \( y = - 2x\)).

Answer:

\( y=-2x \)