Among all the subjects, mathematics is the most complex subject for most people. The reason behind that is every formula seems complicated initially, but when it is understood properly, mathematics becomes the easiest subject. Every person has their own way of explaining a certain thing and every person has their own pace of learning things.
Mathematics gets easier and more complicated depending on the person explaining it. Every formula in mathematics has it own importance and upon changing it even in the slightest manner, it can change everything about it; therefore we have to pay our full attention while learning mathematics.
Mathematics has many topics and for every one of them, there is a formula. One of the topics is called Slope.
A slope is a numerical measure of a line’s horizontal inclination. The slope of a ray, line or any line segment is basically the ratio of the vertical to the horizontal distance between two points, this geometry is called analytic geometry. A slope can also be called a Tangent or a Gradient.
To find the slope of the straight line the formula is written like m=(y2-y1)/(x2-x1) and it is the right way of putting the values. You can’t change the formula m=(x2-x1)/(y2-y1) because it might result in complete failure as it isn’t the right way.
Check out this video to learn how to use the formula in a problem.
The difference between y2,y1,x2,x1 and x2,x1,y2,y1 is that both of these are used for different situations. To find the slope y2,y1,x2,x1 is used which is written like m=(y2-y1)/(x2-x1) and to find the distance between two points x2,x1,y2,y1 is used which is written like d=√((x2-x1)²+(y2-y1)². You can merely switch the values of x1 and y2 with x2 and y2 respectively.
Have a quick look at this video for a better understanding:
If we don’t want to get technical, you can say that y2,y1,x2,x1, and x2,x1,y2,y1 have merely switched their positions. If you know the formulas to find the slope and to find the distance between two points, it doesn’t matter if y2,y1,x2,x1 is written like x2,x1,y2,y1 or vice versa.
What does y2 y1 x2 x1 mean?
As you must know, a rectangular or Cartesian plane has two lines that intersect at right angles at the point O which is called the origin. The horizontal axes are called the x-axis and the vertical axes are called the y-axis.
As every problem has its own formula, to find the slope you have to use a formula which is written as m=(y2-y1)/(x2-x1), you can only change the values of x1 and y1 with x2 and y2 respectively, anymore changes can result in complete failure.
Moreover, the slope of a straight line can be positive, negative, zero, or undefined. If y2 – y1 and x2 – x1 have the same signs then the slope of the straight line will be positive.
Do x1 y1 and x2 y2 numbers matter?
Yes, they do matter, to know what are the coordinates. This way it is easier to put the values in the formula. For example, (3,9) and (7,8) are the coordinates, so we can see that the value of x1 is 3, y1 is 9, x2 is 7, and y2 is 8.
This way it gets easier to put the values in a formula in their right places as each coordinate has its own place.
Without x1 y1 and x2 y2, you might make mistakes by putting in the wrong coordinates which will, of course, result in wrong answers.
Here is the table for different formulas that contains y2,y1,x2,x1 and x2,x1,y2,y1.
| Name of the Formula | Formula |
| To find the distance/length between two points | d=√((x2-x1)²+(y2-y1)² |
| To find the slope | m=(y2-y1)/(x2-x1) |
What is y1 x1 y2 x2 called?
y1 x1 y2 x2 is called a Slope, although some may refer to them as Gradient.
Mathematics can sometimes be challenging as the topic of slope can have many similar formulas. We can mistakenly change the formula which can result in wrong answers. x1 y1 and x2 y2 are the right way which makes y1 x1 and y2 x2 wrong.
When you are given a problem that can be (3,9) and (7,8) you have to put the values in a formula, for example, the formula of slope which is m=(y2-y1)/(x2-x1), now how do you know which is the value of x1 x2 and y1 y2. Well, x1 y1 and x2 y2 is the way to know that, basically, the value of x1 is 3, y1 is 9, x2 is 7, and last but not least y2 is 8.
What happens when you change the formula?
In mathematics, we can’t just change formulas because that can create different outcomes. We can in some cases make changes to the formula, but we aren’t supposed to add anything that doesn’t belong there.
For example, in the formula of finding the distance/length between two points d=√((x2-x1)²+(y2-y1)² you can merely change the position of x1 and y1 with x2 and y2 respectively.
If you change the formula by adding in different things, there are a number of outcomes that you can get:
- Wrong answers.
- Negative, but right result.
- Positive, but wrong answer.
These are the reasons why we can’t change formulas as we want. Although you can change them if you are using them for a different problem, we have to seek help from a mathematician as mathematics is quite complex.
To Conclude
Mathematics tends to get easier or more complicated depending on the person explaining it. As we know, there are many topics in mathematics, and one of them is called Slope. A slope is a numerical measure of a line’s horizontal inclination. The slope/Gradient/Tangent of a ray, line, or any line segment is the ratio of the vertical to the horizontal distance between two points.
The difference between y2,y1,x2,x1 and x2,x1,y2,y1 is both of these are used in different situations. To find the slope y2,y1,x2,x1 is used which is written as m=(y2-y1)/(x2-x1) and to find the distance/length between two points x2,x1,y2,y1 is used which is written as d=√((x2-x1)²+(y2-y1)². You can’t change the formula because it can give wrong answers, you can only switch the values of x1 and y2 with x2 and y2 respectively.
A rectangular or Cartesian plane has two lines that intersect at right angles at the point O which is known as the origin. The horizontal axes are called the x-axis and the vertical axes are called the y-axis. To know which value is put in a formula x1 y1 and x2 y2 helps immensely. For example, (3,9) and (7,8) are the coordinates, so the value of x1 is 3, y1 is 9, x2 is 7, and y2 is 8.
The topic of the slope has many similar formulas. We can mistakenly change the formula which can result in wrong answers. x1 y1 and x2 y2 are the right way and y1 x1 and y2 x2 are wrong.
We aren’t supposed to change formulas because it can result in different outcomes which can be both right and wrong. But, yes you can make a few changes within the formula, for instance, in d=√((x2-x1)²+(y2-y1)² you can switch x1 and y1 with x2 and y2 respectively, other than that you aren’t supposed to change anything else.
Mathematics is difficult, but when you have a firm grasp on the formulas and their uses it can get much easier.
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