Question

23,136 Learners found this answer helpful

modeling parallel and perpendicular lines line ql is represented by the equation $y = x + 1$. line gn is parallel to line ql. the coordinates of point g are $(0, -2)$. determine the equation of line gn in slope - intercept form. $y = x - 2$ (table: slope of line ql $m_1$, slope of line gn $m_2$, point - slope form of line gn $y - y_1 = m(x - x_1)$)

Explanation:

Step1: Find slope of QL

Line QL: \( y = x + 1 \) (slope - intercept form \( y = mx + b \), so slope \( m_1 = 1 \)).

Step2: Determine slope of GN

Parallel lines have equal slopes, so \( m_2 = m_1 = 1 \).

Step3: Use point - slope form

Point \( G(0, - 2) \), point - slope form: \( y - y_1 = m(x - x_1) \). Substitute \( m = 1 \), \( x_1 = 0 \), \( y_1 = - 2 \): \( y - (-2)=1(x - 0) \), simplify to \( y + 2 = x \), then \( y = x - 2 \).

Answer:

Slope of Line QL (\(m_1\)): \(1\)
Slope of Line GN (\(m_2\)): \(1\)
Point - Slope Form of Line GN: \(y - (-2)=1(x - 0)\) (or \(y + 2 = x\))
Equation of Line GN in slope - intercept form: \(y = x - 2\)