Step-by-step explanation:
Two lines are parallel if they have the same slope.
To find the slope of the line that passes through two points, [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex], you can use the following formula:
[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
For the first set of points, [tex](-1, -2)[/tex] and [tex](4, 4)[/tex], we can find the slope with the following:
[tex]\frac{4 - (-2)}{4 - (1)}[/tex]
[tex]\frac{4 + 2}{4 + 1}[/tex]
[tex]\frac{6}{5}[/tex]
For the second set of points, [tex](6, 3)[/tex] and [tex](-1, -3)[/tex], we can find the slope with the following:
[tex]\frac{-3 - 3}{-1 - 6}[/tex]
[tex]\frac{-6}{-7}[/tex]
[tex]\frac{6}{7}[/tex]
Since the two slopes are [tex]\frac{6}{5}[/tex] and [tex]\frac{6}{7}[/tex], the two lines are not parallel.
