Similarities and differences : The similarities between writing an equation for a perpendicular line and a parallel line is that both equations consist of a slope and a y-intercept even if parallel lines never meet.
The difference is that parallel line do not intersect and perpendicular lines do and parallel line have the same slope and perpendicular lines have the opposite slope.
The difference is that parallel line do not intersect and perpendicular lines do and parallel line have the same slope and perpendicular lines have the opposite slope.
Example of Parallel Line :Find the equation of the line that is:
The slope of y=2x+1 is: 2
The parallel line needs to have the same slope of 2.
We can solve it using the "point-slope" equation of a line:
y − y1 = 2(x − x1)
And then put in the point (5,4):
y − 4 = 2(x − 5)
And that answer is OK, but let's also put it in y = mx + b form:
y − 4 = 2x − 10
y = 2x − 6
- parallel to y = 2x + 1
- and passes though the point (5,4)
The slope of y=2x+1 is: 2
The parallel line needs to have the same slope of 2.
We can solve it using the "point-slope" equation of a line:
y − y1 = 2(x − x1)
And then put in the point (5,4):
y − 4 = 2(x − 5)
And that answer is OK, but let's also put it in y = mx + b form:
y − 4 = 2x − 10
y = 2x − 6
Example:Find the equation of the line that is
The slope of y=−4x+10 is: −4 The negative reciprocal of that slope is: m = − 1−4 = 14 So the perpendicular line will have a slope of 1/4: y − y1 = (1/4)(x − x1) And now put in the point (7,2): y − 2 = (1/4)(x − 7) And that answer is OK, but let's also put it in "y=mx+b" form: y − 2 = x/4 − 7/4 y = x/4 + 1/4 |
A baseball field is an example for Perpendicular Lines due to the field intersecting and forming a 90 degree angle from all of the bases.
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A running track is an example of Parallel Lines due to the lines never intersecting and having the same distance and distance between each lane.
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EXPLANATION:
- Parallel Lines- When you write an equation for two Parallel Lines they will both always have the same slope , if they do not they are not parallel , you will then combine the slope with each of the lines y-intercept, which is were the line touches the y-axis.
- Perpendicular Lines- When you are writing the equation for two Perpendicular Lines they will have the opposite reciprocal slope, for example 1/3 and -3. When you have the both slopes you will again add the slope with the y-intercept.
Sources:
Example problems: https://www.mathsisfun.com/algebra/line-parallel-perpendicular.html
Example problems: https://www.mathsisfun.com/algebra/line-parallel-perpendicular.html