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Equations of Parallel & Perpendicular Lines

Equations of Parallel Lines

You can easily calculate a line that is parallel to the line with a know equation. Let us look at the example underneath. The equation of the line is y=x+1 and we know that the blue line crosses the point (2,1). We also know that the slope of the line is two and the we know that the slope of the parallel line also has to be 2. We can use the following formula to calculate the equation of the parallel line. (m is the gradient/slope) Let us substitute the x and y value of the known point into the equation and solve the equation to find the equation of the parallel line. We now know the equation of the blue (parallel) line. By looking at the graph we can see that the equation is correct. If you can look at a graph for finding the equations of parallel lines, then you can solve the problem just by looking at the graph by identifying the y-intercept.

Equations of Perpendicular Lines

We can use coordinate geometry skills to calculate the equations of perpendicular lines. Two perpendicular lines can be identified by looking at the product of their slopes (if it is equal to -1, the lines are perpendicular). The equation of the red (known) line is y=2x+1. We also know that the perpendicular line passes through the point (2,-1). Let us first calculate the slope of the blue (perpendicular) line. The gradient of this line is the negative reciprocal of the red line. Let us calculate the negative reciprocal of the gradient 2. We have identified that the gradient of the perpendicular line is negative a half or -0.5. Let us now use the point-slope equation of a line formula that we have also used before. We now the point on the line and the gradient of the line. As a result, we simply have to substitute the values into the equation and solve it to find the complete equation of the perpendicular line. The final equation of the blue line is y=-0.5x. If you can look at a graph with the two perpendicular lines you can also find the y-intercept by looking at the graph.

More Maths Lessons

You should now be able to master coordinate geometry. You should now look at some other topics such as trigonometry. To select a different topic you can visit our library. Please share this page if you like it or found it helpful!
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(2,1)
(2,-1)
Angles Area & Perimeter Trigonometry 35.0 COORDINATE GEOMETRY 35.1 BASICS OF COORDINATE GEOMETRY 35.2 ADVANCED COORDINATE GEOMETRY
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Chapter 35.3:  Learning Outcomes Students will learn how to find the equations of parallel lines! Students will learn how to find the equations of perpendicular lines!

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