Equations of Slope: X & Y Defining Equation

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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.
  • #1
alliereid
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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?
 
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  • #2
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...
 
  • #3
sin or tan of the angle of slope are both commonly used
 
  • #4
Sometimes the Greek letter Δ is used to signify the change in a quantity or variable. That might be what they are looking for.
 

Related to Equations of Slope: X & Y Defining Equation

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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