Question

Explain how the slopes of two lines in${\mathrm{ℝ}}^2$ can be used to determine whether the lines are parallel or identical. If the two lines are not parallel or identical, what must be true about the lines?

Short answer

Slope of a line is defined as the ratio of difference of $y$coordinates to the difference of $x$ Coordinates. It is denoted by the letter $m$

Step-by-step solution

Step 1:Given information

The slopes of two lines in ${\mathrm{ℝ}}^2$

Step 2:Explaination

Slope of a line is defined as the ratio of difference of $y$coordinates to the difference of $x$Coordinates. It is denoted by the letter $m$.

In ${\mathrm{ℝ}}^2$, if the slopes of two lines is equal then the lines are either parallel or identical.

When the slopes of two lines in ${\mathrm{ℝ}}^2$that are not either parallel or identical intersect at a unique point.