Question

1. # What Is The Equation Of The Line That Passes Through (–2, –3) And Is Perpendicular To 2X – 3Y = 6?

When it comes to equations of lines, there are a few basic concepts that you should know. One of these concepts is how to determine the equation of the line that passes through two given points and is perpendicular to another given line. This can be an important skill to master for geometry and algebra classes, as well as for applications in mathematics, engineering, physics and other fields. In this blog post, we will explore this concept in detail. Specifically, we will look at what the equation of the line that passes through a specific point (-2,-3) and is perpendicular to 2x-3y=6 would be. We will also discuss why knowing how to solve problems like this can be so useful.

## What is the equation of a line?

There are an infinite number of lines that pass through the point (–, –) and are perpendicular to the line x – y = 0. To find the equation of one of these lines, we can use the point-slope form of a line:

y – y1 = m(x – x1)

Where m is the slope of the line and (x1, y1) is any point on the line. The slope of a line perpendicular to x – y = 0 is m = -1. So, plugging in our values, we get:

y – (-) = -(x – (-))
y + = -x +
y = x

## What is the equation of a line that passes through two points?

To find the equation of a line that passes through two points, you need to use the slope formula. The slope formula is:

m = (y2 – y1) / (x2 – x1)

To use the slope formula, plug in the coordinates of the two points you are using. For example, if you were finding the equation of a line that passes through (-2, 3) and (4, 7), you would plug those numbers into the formula like this:

m = (7 – 3) / (4 – (-2))
= 4 / 6
= 2/3

## What is the equation of a line that is perpendicular to another line?

Assuming you are talking about the equation of a line in slope-intercept form, the equation of a line that is perpendicular to another line would have a slope that is the negative reciprocal of the other line. So, if the equation of the other line is y = mx + b, the equation of the perpendicular line would be y = -1/mx + b.

## How to solve for the equation of a line that passes through (–2, –3) and is perpendicular to 2X – 3Y = 6

To solve for the equation of a line that passes through (–2, –3) and is perpendicular to 2X – 3Y = 6, we need to find the slope of the given line and then use the slope to find the equation of the desired line. The slope of the given line is m = -2/3. This means that the equation of the desired line will have a slope of -1/m, or 3/2. To find the equation of this line, we can use any point on the line and plug it into the standard form equation for a line: y-y1=m(x-x1). In this case, we’ll use (–2, –3) as our point: -3-(-2)=m(-2-(-2)), or 3=-(3/2)(-4), which simplifies to 3=6. So, our final equation is 6Y – 12X = 18.

## Conclusion

We have now seen how to find the equation of a line that passes through a given point and is perpendicular to another line. We started by finding the gradient of the perpendicular line, which we found was -2/3, then applied it to our formula for lines going through points y=mx+c. By plugging in our coordinates from (–2, –3) we arrived at an answer of 3x + 2y = –15. This equation can be used to represent any line that passes through (–2, –3) and is perpendicular with 2x – 3y = 6.

2. What Is The Equation Of The Line That Passes Through (–2, –3) And Is Perpendicular To 2X – 3Y = 6?

If you’re a math student, you’ve probably come across the equation of a straight line before. It’s important to understand this concept for many purposes, such as plotting graphs and finding the intercepts of a line. In this article, we’ll look at the equation of the line that passes through (–2, –3) and is perpendicular to 2X – 3Y = 6.

We can use a few methods to calculate the equation of a line, but the most common is the slope-intercept form. This form takes the following form:

Y = mX + b

In this equation, m is the slope of the line and b is the y-intercept. The slope is the number that describes the steepness of the line. In other words, it is the number that specifies how much the y-coordinate changes when the x-coordinate changes by one.

To calculate the equation of the line that passes through (–2, –3) and is perpendicular to 2X – 3Y = 6, we need to find the slope of the line first. Let’s take a look at the given equation and solve for its slope:

2X – 3Y = 6

Divide both sides by 2:

X – 1.5Y = 3

Divide both sides by -1.5:

-X + Y = -2

We can now see that the slope of the line is -1. That means the line is a vertical one, and its equation is:

Y = -X + b

We can now find the y-intercept b. The y-intercept is the point at which the line intersects the y-axis. To find b, we can substitute the coordinates of the given point (–2, –3) into the equation and solve for b:

-2 = -(-2) + b

2 = b

Therefore, the equation of the line that passes through (–2, –3) and is perpendicular to 2X – 3Y = 6 is Y = -X + 2.