OK, now we have our slope, which is 4. As mentioned above, the slopes of perpendicular lines are negative reciprocals of each other. So, if we know the slope of a line perpendicular to our line, we have it made. Practice Problems These are practice problems to help bring you to the next level. It will allow you to check and see if you have an understanding of these types of problems.
Math works just like anything else, if you want to get good at it, then you need to practice it. Even the best athletes and musicians had help along the way and lots of practice, practice, practice, to get good at their sport or instrument. In fact there is no such thing as too much practice.
At the link you will find the answer as well as any steps that went into finding that answer. Practice Problems 1a - 1c: Find the slope of the line that is a parallel and b perpendicular to the given line. Need Extra Help on these Topics? All rights reserved. After completing this tutorial, you should be able to: Find the slope of a line that is parallel to a given line.
This tutorial looks at the relationship between the slopes of parallel lines as well as perpendicular lines. In other words, perpendicular slopes are negative reciprocals of each other. If you need more of a review on how to use this form, feel free to go to Tutorial Equations of Lines. If your linear equation is written in this form, m represents the slope and b represents the y -intercept.
Example 1 : Find the slope of any line that is a parallel and b perpendicular to the line. Before we tackle finding the parallel and perpendicular slopes it really can help us out if we find the slope of the given line. Lining up the form with the equation we have been given, can you see what the slope is? Example 2 : Find the slope of the line that is a parallel and b perpendicular to the line.
Lining up the form with the equation we got, can you see what the slope is? Example 3 : Find the slope of the line that is a parallel and b perpendicular to the line. Do you remember what special type of line this equation is? It is a vertical line. If you need a review on vertical lines, feel free to go to Tutorial Graphing Lines. The final equation for the line will be. What line is parallel to and passes through the point?
The slope of this line is. A parallel line will have the same slope. Now that we know the slope of our new line, we can use slope-intercept form and the given point to solve for the y-intercept. What is the equation of a line that is parallel to the line and includes the point? The line parallel to must have a slope of , giving us the equation.
To solve for b , we can substitute the values for y and x. Therefore, the equation of the line is. What line is parallel to , and passes through the point? For parallel lines, the slopes must be equal, so the slope of the new line must also be. We can plug the new slope and the given point into the slope-intercept form to solve for the y-intercept of the new line. What line is parallel to at?
Find the slope of the given line: slope intercept form. Parallel lines have the same slope, so now we need to find the equation of a line with slope and going through point by substituting values into the point-slope formula.
Thus, the new equation is. Which of these formulas could be a formula for a line perpendicular to the line? This is a two-step problem. First, the slope of the original line needs to be found. The slope will be represented by " " when the line is in -intercept form. So the slope of the original line is.
A line with perpendicular slope will have a slope that is the inverse reciprocal of the original. So in this case, the slope would be. The second step is finding which line will give you that slope. For the correct answer, we find the following:. So, the slope is , and this line is perpendicular to the original. Which of the following is a line that is parallel to the line defined by the equation? Since parallel lines have equal slopes, you should find the slope of the line given to you.
The easiest way to do this is to solve the equation so that its form is. Take your equation:. First, subract from both sides:. Next, subtract from both sides:. Finally, divide by :. Thus, your slope is. Among the options provided only is parallel. Solve this equation as well for form. First, subtract from both sides:. Then, divide by :. Both lines can go onto infinity, and they will never meet. Let's look at an example. A line parallel to this will have the same slope and a different intercept.
There are essentially an infinite number of options. One special property shared by parallel lines is that the slopes are equivalent. Intersecting lines will never have equal slope. Parallel lines' slopes are equivalent, so the only thing setting them apart from equivalent lines is the difference in y-intercept. If you keep the slope of a line the same but change the y-intercept, you're basically moving the line uniformly all points by the same amount in a vertical direction. The two lines won't intersect, so we call them parallel.
Lines that meet at a 90o angle are perpendicular. The perpendicular slope are opposite reciprocals of the parallel slope. The two lines are parallel: they have the same slope, 0.
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