How to Figure out if Two Lines Are Parallel
Define the formula for slope., Identify the X and Y coordinates of two points on each line., Plug the points for each line into the slope formula., Compare the slopes of each line.
Step-by-Step Guide
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Step 1: Define the formula for slope.
The slope of a line is defined by (Y2
- Y1)/(X2
- X1) where X and Y are the horizontal and vertical coordinates of points on the line.
You must define two points on the line to calculate this formula.
The point closer to the bottom of the line is (X1, Y1) and the point higher on the line, above the first point, is (X2, Y2).This formula can be restated as the rise over the run.
It is the change in vertical difference over the change in horizontal difference, or the steepness of the line.
If a line points upwards to the right, it will have a positive slope.
If the line is downwards to the right, it will have a negative slope. -
Step 2: Identify the X and Y coordinates of two points on each line.
A point on a line is given by the coordinate (X, Y) where X is the location on the horizontal axis and Y is the location on the vertical axis.
To calculate the slope, you need to identify two points on each of the lines in question.Points are easily determined when you have a line drawn on graphing paper.
To define a point, draw a dashed line up from the horizontal axis until it intersects the line.
The position that you started the line on the horizontal axis is the X coordinate, while the Y coordinate is where the dashed line intersects the line on the vertical axis.
For example: line l has the points (1, 5) and (-2, 4) while line r has the points (3, 3) and (1,
-4). , To actually calculate the slope, simply plug in the numbers, subtract, and then divide.
Take care to plug in the coordinates to the proper X and Y value in the formula.
To calculate the slope of line l: slope = (5 – (-4))/(1 – (-2)) Subtract: slope = 9/3 Divide: slope = 3 The slope of line r is: slope = (3 – (-4))/(3
- 1) = 7/2 , Remember, two lines are parallel only if they have identical slopes.
Lines may look parallel on paper and may even be very close to parallel, but if their slopes are not exactly the same, they aren’t parallel.In this example, 3 is not equal to 7/2, therefore, these two lines are not parallel. -
Step 3: Plug the points for each line into the slope formula.
-
Step 4: Compare the slopes of each line.
Detailed Guide
The slope of a line is defined by (Y2
- Y1)/(X2
- X1) where X and Y are the horizontal and vertical coordinates of points on the line.
You must define two points on the line to calculate this formula.
The point closer to the bottom of the line is (X1, Y1) and the point higher on the line, above the first point, is (X2, Y2).This formula can be restated as the rise over the run.
It is the change in vertical difference over the change in horizontal difference, or the steepness of the line.
If a line points upwards to the right, it will have a positive slope.
If the line is downwards to the right, it will have a negative slope.
A point on a line is given by the coordinate (X, Y) where X is the location on the horizontal axis and Y is the location on the vertical axis.
To calculate the slope, you need to identify two points on each of the lines in question.Points are easily determined when you have a line drawn on graphing paper.
To define a point, draw a dashed line up from the horizontal axis until it intersects the line.
The position that you started the line on the horizontal axis is the X coordinate, while the Y coordinate is where the dashed line intersects the line on the vertical axis.
For example: line l has the points (1, 5) and (-2, 4) while line r has the points (3, 3) and (1,
-4). , To actually calculate the slope, simply plug in the numbers, subtract, and then divide.
Take care to plug in the coordinates to the proper X and Y value in the formula.
To calculate the slope of line l: slope = (5 – (-4))/(1 – (-2)) Subtract: slope = 9/3 Divide: slope = 3 The slope of line r is: slope = (3 – (-4))/(3
- 1) = 7/2 , Remember, two lines are parallel only if they have identical slopes.
Lines may look parallel on paper and may even be very close to parallel, but if their slopes are not exactly the same, they aren’t parallel.In this example, 3 is not equal to 7/2, therefore, these two lines are not parallel.
About the Author
Michelle Watson
A passionate writer with expertise in lifestyle topics. Loves sharing practical knowledge.
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