Q .7. - Calculus

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? 

Step-by-Step Solution

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 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.