Question

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. $y = \square$

Explanation:

Step1: Find slope of QL

The equation of line QL is \( y = x + 1 \), which is in slope - intercept form \( y=mx + b \) (where \( m \) is the slope and \( b \) is the y - intercept). So the slope of line QL, \( m_1=1 \).

Step2: Determine slope of GN

Since line GN is parallel to line QL, parallel lines have equal slopes. So the slope of line GN, \( m_2 = m_1=1 \).

Step3: Use point - slope form

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 the point \( G(0,-2) \) lies on line GN, so \( x_1 = 0 \), \( y_1=-2 \) and \( m = 1 \). Substituting these values into the point - slope form:
\( y-(-2)=1\times(x - 0) \)
Simplify the left - hand side: \( y + 2=x \)

Step4: Convert to slope - intercept form

Subtract 2 from both sides of the equation \( y + 2=x \) to get it in slope - intercept form (\( y=mx + b \)):
\( y=x-2 \)

Answer:

\( y = x - 2 \)