Question

1. # Which Equation Is The Equation Of A Line That Passes Through (-10 3) And Is Perpendicular To Y=5X-7

When first learning algebra, the equation of a line is one of the most important concepts to master. It helps students understand basic geometry and how to graph lines in different situations. But what happens when you are presented with an equation of a line that passes through two points and is perpendicular to another? This can be a tricky concept to wrap your head around, but it isn’t impossible. In this blog post we will explore which equation is the equation of a line that passes through (-10 3) and is perpendicular to y=5x-7.

## The Slope-Intercept Form of a Line

The slope-intercept form of a line is y=mx+b, where m is the slope and b is the y-intercept. In order to find the equation of a line that passes through (-3,4) and is perpendicular to y=x-1, we can use the point-slope form of a line. The point-slope form of a line is y-y1=m(x-x1), where (x1,y1) is any point on the line and m is the slope. We know that the slope of a perpendicular line is the negative reciprocal of the slope of the original line, so in this case, the slope would be -1. We also know that the y-intercept must be 4, since that’s one of our given points. So our final equation would be y=-x+4.

## The Point-Slope Form of a Line

In mathematics, the point-slope form of a line is an equation of a line that passes through a given point and has a given slope. The general form of the equation is y = mx + b, where m is the slope and b is the y-intercept. Given a point (x1, y1) and a slope m, the point-slope form of the equation of the line through (x1, y1) with slope m is:

y – y1 = m(x – x1)

This can be rewritten as:

y = mx – mx1 + y1

The advantage of using the point-slope form is that it is very easy to find the equation of a line when you know its slope and one point that it passes through.

## The Standard Form of a Line

A line can be represented in various forms, but the most common form is the standard form of a line. The standard form of a line is represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. In order to find the equation of a line that passes through (-3,4) and is perpendicular to y=x-1, we need to find the slope of the given line and then use the point-slope form of a line. The point-slope form of a line is represented by the equation y – y1 = m(x – x1), where m is the slope of the line and (x1,y1) is any point on the line. In our case, we can choose (0,-1) as our point since it lies on both lines. Plugging in our values, we get: y – (-1) = -1(x – 0), which simplifies to y + 1 = -x. Therefore, the equation of our desired line is y = -x + 1.

## How to Find the Equation of a Line That Passes Through Two Points

To find the equation of a line that passes through two points, we need to find the slope of the line and then use that slope to write the equation. To find the slope, we need to use the formula:

Slope = (y2-y1)/(x2-x1)

In this formula, “y2” and “y1” are the y-coordinates of the two points, and “x2” and “x1” are the x-coordinates of the two points. Once we have the slope, we can use it to write the equation of the line in slope-intercept form:

y = mx + b

In this equation, “m” is the slope and “b” is the y-intercept. To find “b”, we just need to plug one of our points into the equation and solve for “b”.

## How to Find the Equation of a Perpendicular Line

Assuming you already know how to find the equation of a line in slope-intercept form, finding the equation of a perpendicular line is simply a matter of finding the negative reciprocal of the original line’s slope and solving for y. For example, if we have the line y=2x+5 and we want to find a perpendicular line that passes through the point (-1, 3), we would first take the negative reciprocal of 2 (which is -1/2) and plug it into our equation as follows: y=-1/2x+b. We can then solve for b by plugging in our known point (-1, 3) and solving for b:

3=-1/2(-1)+b
3=1/2+b
3.5=b

Therefore, our final equation is y=-1/2x+3.5

## Conclusion

As we can see, the equation for a line that passes through (-10 3) and is perpendicular to y=5x-7 is y=-1/5 x + 13. The process of finding this equation is straightforward as long as you have a basic understanding of how linear equations work. Knowing how to solve problems like these will give you an advantage when it comes to solving math problems in the future.

2. It’s a simple question with a straightforward answer – but it can be difficult to know where to start if you’re not familiar with equations of a line. Fortunately, help is here!

Are you ready to find out which equation is the equation of a line that passes through (-10 3) and is perpendicular to y=5x-7?

Let’s break it down. We know that a line is defined by an equation of the form y=mx+b, where m is the slope of the line and b is the y-intercept. The slope of a line tells us how “steep” the line is, and the y-intercept tells us where the line crosses the y-axis.

To find the equation of a line that passes through a given point and is perpendicular to a second line, we must first find the slope of the line that passes through the point. To do this, we can use the “slope-intercept form” of the equation of a line: y = mx + b.

Plugging in the coordinates of our point (-10 3), we find that the slope of the line is -3/10.

Now that we know the slope of the line, we can use the equation of the second line (y=5x-7) to find the equation of the line that is perpendicular to it. To do this, we simply need to find the negative reciprocal of the slope of the second line. This is easy to do – simply flip the fraction and make it negative.

In this case, we find that the slope of the line perpendicular to y=5x-7 is 10/3.

Now that we have the slope of the line, we can use the slope-intercept form of the equation of a line to find the equation of the line that passes through the given point and is perpendicular to y=5x-7. Plugging in the slope (10/3) and the coordinates of the given point (-10 3) into the equation, we find that the equation of the line is:

y = (10/3)x – 30

There you have it – the equation of a line that passes through (-10 3) and is perpendicular to y=5x-7 is y = (10/3)x – 30.

We hope this has been helpful!