Question

1. use the graph on the right to answer the two questions below.

a. what is an equation of the line that passes through point g and is parallel to line p?
b. what is an equation of the line that passes through point g and is perpendicular to line p?

Explanation:

Step1: Find the slope of line p

Let's assume two points on line p, say $(x_1,y_1)$ and $(x_2,y_2)$. If we count the rise - over - run, for example, if it goes up 2 units and right 1 unit, the slope of line p, $m_p = 2$.

Step2: Find the equation of the parallel line

Parallel lines have the same slope. Let the coordinates of point G be $(x_G,y_G)$. Using the point - slope form $y - y_1=m(x - x_1)$, with $m = m_p=2$ and $(x_1,y_1)=(x_G,y_G)$, we get $y - y_G=2(x - x_G)$.

Step3: Find the slope of the perpendicular line

The slope of a line perpendicular to a line with slope $m$ is $m'=-\frac{1}{m}$. Since $m = 2$ for line p, the slope of the perpendicular line, $m_{perp}=-\frac{1}{2}$.

Step4: Find the equation of the perpendicular line

Using the point - slope form $y - y_1=m(x - x_1)$ with $m = m_{perp}=-\frac{1}{2}$ and $(x_1,y_1)=(x_G,y_G)$, we get $y - y_G=-\frac{1}{2}(x - x_G)$.

Answer:

a. $y - y_G=2(x - x_G)$
b. $y - y_G=-\frac{1}{2}(x - x_G)$