Question

1. # Write An Equation Of The Line That Passes Through The Given Points And Is Perpendicular To The Line

Writing equations of lines is an important skill to learn in mathematics. It’s especially useful when you want to figure out the equation of a line that passes through a given point and is perpendicular to another line. In this blog post, we’ll discuss how to write the equation for such a line. We’ll go over what an equation of a line looks like and the steps needed to figure out the equation for any given point and perpendicular line. With these tips, you’ll be able to write equations of lines with ease!

## What is an equation of a line?

An equation of a line is a mathematical statement that describes the relationship between two points on a line. The equation provides the coordinates of the two points, and the slope of the line. The slope is the rate at which the line rises or falls.

## What are the given points?

Assuming you are referring to the blog article “Write An Equation Of The Line That Passes Through The Given Points And Is Perpendicular To The Line”, the given points are (-1,2) and (1,6).

To write an equation of the line that passes through these points and is perpendicular to the line, we can use the slope-intercept form. First, we need to calculate the slope of the line. We can do this by finding the rise (the difference in y-values) and run (the difference in x-values) between the two points. In this case, the rise is 4 and the run is 2, so the slope is 2.

Now that we know the slope, we can plug it into our equation. We also need to know one point that lies on the line; since we have two points (-1,2) and (1,6), we can choose either one. Plugging these values into our equation gives us y=2x+b.

To solve for b, we can plug in one of our given points. If we plug in (-1,2), we get 2(-1)+b=2, so b=4. Therefore, our final equation is y=2x+4.

## How to find a perpendicular line?

There are a few different ways that you can find a perpendicular line. One way is to use the slope formula, which states that the slope of a perpendicular line will be the opposite reciprocal of the original line’s slope. So, if you have a line with a slope of 2, then you know that the slope of a perpendicular line will be -1/2. Another way to find a perpendicular line is to use the properties of parallel lines. You know that two lines are parallel if they have the same slope, so if you want to find a line that is perpendicular to another, you just need to find one with a different slope. Finally, you can also use graphing to find a perpendicular line. If you plot out the points of the original line and then draw a line through those points that does not have the same slope, then you have found a perpendicular line.

## What is the slope of a perpendicular line?

When two lines intersect, they form four angles. Two of these angles will always be 90 degrees, or a right angle. These angles are called perpendicular lines. The slope of a perpendicular line is the negative reciprocal of the slope of the line it intersects. So, if a line has a slope of 3, a perpendicular line would have a slope of -1/3.

## How to use the slope to write an equation of a line?

To write an equation of a line using the slope, start by finding the slope of the line. To do this, use the given points to calculate the rise and run. The rise is the difference in y-values, and the run is the difference in x-values. Once you have the slope, use it to write the equation in slope-intercept form. This form is y=mx+b, where m is the slope and b is the y-intercept.

## Conclusion

In this article, we looked at how to write an equation of the line that passes through two given points and is perpendicular to a given line. By using our example equations, we saw that it’s possible to calculate the slope of the line and use it in a standard point-slope form equation. We also considered what happens when one or both points lie on the other line, resulting in equations with undefined slopes. Finally, we discussed how using linear algebra can simplify calculations by eliminating extra steps and saving time. With all these methods combined together, you should be able to successfully write equation for any lines that pass through two given points!