Question

Determine if the lines below are parallel. Explain your reasoning

Answer 1

the lines are parallel

Step-by-step 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{ = }(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{ = }(1-4)/(0-(-2))=(-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{ = }(1-7)/(4-0)=(-6)/(4) \\ m\text{ = -3/2} \end{gathered}`

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