# Slope Essay

Essay by PaperNerd ContributorCollege, Undergraduate September 2001

Slope Essay For years Mathematicians have studied and found various mathematical equations. One thing they've came across is numerous equations for slope. You maybe asking, what is slope? Slope is rise over run.

To find slope (m=slope) on a graph, you draw and label your x (horizontal) and y (vertical) axis on a xy-coordinate plane. When you draw your two lines they should meet at right angles at a point zero. The axis is divided into four quadrants. Then you find any two points ( (0,0) and (2,1) ) on a line and calculate rise over run (m=2/1). Plot the point on the designated spot which you have calculated.

To find the slope of a line using the coordinates of two points, you find to points using the formula: y-y /x-x . Take the y's and subtract them, then take the x's and subtract them. Then that's your slope.

If it turns out to be zero its no slope and if zero is on the bottom of the fraction it is then called null set, which means a set with no numbers.

Next, you can also find slope by using slope-intercept form, which you us the equation y=mx+b. M = slope, b = y-intercept, and x and y are your points. You will take your slope and plug it into the m and then take the y-intercept and plug it into b. You want to get your y and x on the same side. You can subtract the x to get it over on the y side or you can subtract the y and get in on the x side. Then on one side you should have just a number. It's best to subtract from the side with one variable and one number. The answer should always be in standard form.

Last, but not least you can also find slope using a line by the standard form equation.

(y, y )= m(x, x ) is the standard form equation. There are many ways you can use this equation, to find slope of two points, given a slope and a point, given slope and y-intercept, and slope of parallel and perpendicular lines. In standard form the number before X has to be positive. Also to write an equation you have to know slope and a point. When finding an equation in standard form of a line containing two points and slope use point slope form (y, y )= m(x, x ) and plug in points into the x and y containing the number one next to it and also plug in the slope. When given a fraction for slope, you multiply by the reciprocal on both sides of the equation. Then multiply as usual. Then put in standard form and that's your answer. When finding an equation using two given points you find the slope by subtracting the y's and then the x's as you where illustrated in paragraph three. Then plug one set of the points and the slope into this equation (y, y )= m(x, x ) and work it out. As you did in with the equation before. Your answer should be in standard form. By using slope and y-intercept you use this equation: y=mx+b. You plug in the slope to the m and the y-intercept into the b. Then get the x and y on the same side by adding or subtracting, depending on wether it is a negative or a positive on which you will use.

When Graphing the appearance of lines can be one of four things. It can be a positive, negative, zero, or undefined slope. The Positive slope will be going up and the negative will be going down. As for zero it will be going horizontal and the undefined will go vertical.