Given:
Line a: (3,1) and (8,6)
Line b: (-6,1) and (2,9)
To determine if the given points of two lines if the lines are parallel, perpendicular, or neither, we find the slope of line a first using the slope formula below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where:
m=slope
Based on line a, we let:
We plug in what we know:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{6-1}{8-3} \\ \text{Simplify} \\ m=\frac{5}{5} \\ m=1 \end{gathered}[/tex]Hence, the slope of line a is 1.
Next, we get the slope of line b using the same slope formula and let:
So,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{9-1}{2-(-6)} \\ \text{Simplify} \\ =\frac{9-1}{2+6} \\ =\frac{8}{8} \\ m=1 \end{gathered}[/tex]Hence, the slope of line b is 1.
We also note that parallel lines have the same slope. In addition, the perpendicular slope is the opposite reciprocal of the slope of the line to which it is perpendicular.
Therefore, the answers are:
What is the slope of line a? 1
What is the slope of line b ? 1
Are the slopes opposite reciprocals? No
Are the lines parallel, perpendicular, or neither? Parallel
