Question

determine if the lines below are parallel. Explain your reasoning

Answer 1

the lines are parallel

Explanation:

For the two lines to be parallel, their slopes must be equal

So we would find the slope of both lines and compare:

Dark blue line: using points are (-2, 4) and (0, 1)

$m\text{ = }\frac{y_2-y_1}{x_2-x_1}$$\begin{gathered} x_1=-2,y_1=4,x_2=0,y_2\text{ = 1} \\ m\text{ = }\frac{1-4}{0-(-2)}=\frac{-3}{0+2} \\ m\text{ = -3/2} \end{gathered}$

Light blue line: using points are (0, 7) and (4, 1)

$\begin{gathered} x_1=0,y_1=7,x_2=4,y_2\text{ = 1} \\ m\text{ = }\frac{1-7}{4-0}=\frac{-6}{4} \\ m\text{ = -3/2} \end{gathered}$

Since the slope are the same = -3/2, the lines are parallel