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.

slope of line ql: m1
slope of line gn: m2
point - slope form of line gn: y - y1 = m(x - x1), y - (-2)=x - 0

Explanation:

Step1: Identify slope of parallel lines

Parallel lines have equal slopes. The equation of line QL is $y = x+1$, which is in the form $y=mx + b$ (where $m$ is the slope and $b$ is the y - intercept). So the slope of line QL, $m_1 = 1$. Since line GN is parallel to line QL, the slope of line GN, $m_2=1$.

Step2: Use point - slope form to find line GN equation

The point - slope form of a line is $y - y_1=m(x - x_1)$. We know that a point on line GN is $(0,-2)$ and $m = 1$. Substituting $x_1 = 0$, $y_1=-2$ and $m = 1$ into the point - slope form, we get $y-(-2)=1(x - 0)$, which simplifies to $y + 2=x$ or $y=x - 2$.

Answer:

The slope of line QL is $1$. The slope of line GN is $1$. The equation of line GN in slope - intercept form is $y=x - 2$.