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{{ printedBook.courseTrack.name }} {{ printedBook.name }} Two lines are parallel if their slopes are identical. Thus, we should find the slopes of the lines using the slope formula. $m=x_{2}−x_{1}y_{2}−y_{1} $ If we start with line $A,$ we identify two points on the line.

Note that when choosing points to substitute for $(x_{1},y_{1})$ and $(x_{2},y_{2}),$ it doesn't matter which points on the line you choose, since the result will be the same. Now, we substitute the points into the slope formula.$m=x_{2}−x_{1}y_{2}−y_{1} $

$m=0−(-2)2−0 $

Evaluate right-hand side

$m=1$

The points are now used in the slope formula.

Line | Points | Slope |
---|---|---|

$B$ | $(0,0)$ & $(2,2)$ | $2−02−0 =1$ |

$C$ | $(0,-3)$ & $(4,2)$ | $4−02−(-3) =1.25$ |

Now that we've identified the slope of each line, we can see that $A$ and $B$ have the same slope, so they are parallel.