# Equations of Slope: X & Y Defining Equation

• alliereid
In summary, the defining equation of slope is m = (y2 - y1)/(x2 - x1). The two common forms of the mathematical equation for slope involving X and Y are rise/run = m and (Y2-Y1)/(X2-X1) = m. Another form could be the derivative (slope) at a particular point, such as f'(x) = 2x^2 + 1 at the point where x=2, where both x and y values are known. The Greek letter Δ is also sometimes used to represent the change in a quantity or variable when discussing slope.
alliereid
What is the defining equation of the concept of slope?

I thought it could be rise / run = m or Y2-Y1 / X2-X1 = m but then the next question asks to give the two common forms of the mathematical equation for slope involving X and Y? So would that not be those two equations?

I would say the the equation they are looking for would be:

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

Not sure what the other one would be...Unless you're doing calculus in which case it could be the derivative (slope) at a particular point.

eg. f'(x) = 2x^2 + 1 at the point where x=2

Therefore you have both your 'x' value and 'y' value because technically f(x) = yHope that helped...

sin or tan of the angle of slope are both commonly used

Sometimes the Greek letter Δ is used to signify the change in a quantity or variable. That might be what they are looking for.

## 1. What is the equation for finding the slope of a line?

The equation for finding the slope of a line is y = mx + b, where m represents the slope and b represents the y-intercept.

## 2. How do you find the slope of a line using two given points?

To find the slope of a line using two given points, you can use the slope formula:
m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

## 3. Can the slope of a line be negative?

Yes, the slope of a line can be negative. A negative slope means that the line is decreasing from left to right.

## 4. How do you determine if two lines are parallel or perpendicular?

If two lines have the same slope, they are parallel. If the product of their slopes is -1, they are perpendicular.

## 5. What is the relationship between the slope and steepness of a line?

The slope of a line represents the steepness of the line. A larger slope value means a steeper line, and a smaller slope value means a less steep line. A slope of 0 indicates a horizontal line, and a slope of undefined represents a vertical line.

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