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.

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

Explanation:

Step1: Find slope of line QL

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's assume two points on line QL from the graph. If we take two points $(x_1,y_1)$ and $(x_2,y_2)$ on line QL, say $(-9, - 12)$ and $(0, - 3)$. Then $m_1=\frac{-3-(-12)}{0 - (-9)}=\frac{-3 + 12}{0+9}=\frac{9}{9}=1$.

Step2: Find slope of line GN

Since line GN is parallel to line QL, parallel lines have equal slopes. So $m_2 = 1$.

Step3: Write point - slope form of line GN

The point - slope form of a line is $y - y_1=m(x - x_1)$. The coordinates of point G are $(0,-2)$. Using $m = 1$, $x_1=0$ and $y_1=-2$, we get $y-(-2)=1(x - 0)$, which simplifies to $y + 2=x$ or $y=x - 2$.

Answer:

Slope of Line QL ($m_1$): 1
Slope of Line GN ($m_2$): 1
Point - Slope Form of Line GN: $y+2=x$ (or $y=x - 2$)