One line passes through the points

Question

\[\blueD{(-7,5)}\] and
\[\blueD{(-1,-3)}\]. Another line passes through points
\[\greenD{(0,3)}\] and
\[\greenD{(3,-1)}\].
Are the lines parallel, perpendicular, or neither?

Answer 1

The slopes of the two lines can be found using the slope formula: $m = \frac{y_2-y_1}{x_2-x_1}$.

For the blue line, the two points are $(-7,5)$ and $(-1,-3)$, so the slope is $m_1 = \frac{-3-5}{-1-(-7)} = \frac{-8}{6} = \frac{-4}{3}$.

For the green line, the two points are $(0,3)$ and $(3,-1)$, so the slope is $m_2 = \frac{-1-3}{3-0} = \frac{-4}{3}$.

Since the two slopes are equal, the lines are \boxed{\text{neither parallel nor perpendicular}}.