Posts Tagged ‘slope’
Friday, November 20th, 2009
How to Pick Variables
Description
A detailed tutorial on how to pick variables. Step by step tutorial including several examples of how to pick variables for reference.
Overview
Variables are letters picked to represent unknown values in expressions and equations. Usually they are lowercase, but they can be made uppercase. When trying to pick a variable, you must choose wisely. x is the most common variable, followed by n. x is picked because people associate it with the unknown, and n is picked because it stands for “number.” The variable should be easily recognizable – you should not use a variable that looks like another number or some symbol of a mathematical operation. You should check to see what is included in your equation – for instance, m stands for slope, so if you are doing an equation with slope you need to pick a different variable to avoid confusion. And you should always pick a variable that makes sense – the first letter of your subject matter usually works quite well.
Tags: a, algebra, b, c, choose, equation, expression, lowercase, m, mathematical, n!, number, operation, slope, symbol, unknown, uppercase, value, variable, variables, x, y, z
Posted in Algebra | No Comments »
Friday, November 13th, 2009
Overview of Negative Slopes
Description
A detailed tutorial on negative slopes. Step by step tutorial including several example problems with negative slopes for reference.
Overview
A negative slope is very similar to a positive slope. It is still in the form of rise over run, and it makes no real difference in an equation if a slope is negative or positive. What it does is change the way you graph it. A positive slope you go up and the to the right. In a negative slope, you will either go up and to the left or down and to the right, depending on if the rise or the run is negative. The main mistake that people make with a negative slope is thinking if they see a negative sign, the slope is definitely negative. This is not true. A negative rise and a negative run actually equals a positive slope, you graph it as going down and going to the left, which still creates a positive slope – and in mathematics, two negatives make a positive.
Tags: diagonal, down, graph, horizontal, left, negative, positive, right, rise, run, slope, up, vertical
Posted in Algebra | No Comments »
Friday, October 9th, 2009
Introduction to Zero and Undefined Slopes
Description
Detailed tutorial on undefined and zero slopes. Step by step tutorial including several examples of zero and undefined slopes for reference.
Overview
Zero and undefined slopes are both slopes that do have a definite value to them. They represent very uinigue graphs and lines. A zero slope is a slope of zero over anything – meaning it has a run, but no rise. It is a zero slope because zero divided by anything is simply zero. Zero slopes form horizontal lines. An undefined slope is a slope of anything over zero – meaning it has a rise, but no run. It is an undefined slope because nothing can be divided by zero. Undefined slopes form vertical lines.
Tags: arithmetic, graph, horizontal, line, Math, rise, run, slope, undefined, value, vertical, zero
Posted in Arithmetic | No Comments »
Thursday, September 24th, 2009
An Overview of Rolle’s Theorem
Description
A detailed tutorial on how to solve problems using Rolle’s Theorem. Step by step tutorial including examples of how to solve problems using Rolle’s Theorem for reference.
Overview
Rolle’s Theorem is a special instance of the Mean Value Theorem, and can be used to prove the Mean Value Theorem. Rolle’s Theorem states that a differentiable and continuous function, which attains equal values at two points, must have a point somewhere between them where the slope of the tangent line to the graph of the function is zero. Mathematically this can be expressed as if a real-valued function f is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists a c in the open interval (a, b) such that f ‘(c) = 0.
Tags: Calculus, closed, continuous, differentiable, function, graph, interval, Math, mean value theorem, open, real-valued function, rolle's theorem, slope, tangent line, zero
Posted in Calculus | No Comments »
Thursday, September 17th, 2009
Explanation of the Monotonicity Theorem
Description
A detailed tutorial on the solving of the Monotonicity Theorem. Step by step tutorial including several examples of how to solve the Monotonicity Theorem for reference.
Overview
The Monotonicity Theorem is used to determine if a function is increasing or decreasing. The Monotonicity Theoream states that:
If f ‘(x) > 0 the function is increasing
If f ‘(x) < 0 the function is decreasing
This is basically a repeat of information you already know. The derivative is the same as the slope of a line, and it is obvious to anyone who has spent time studying grpahs that a positive slope increases and a negative slope descreases. Simply find your function, take a derivative, and set it to either less than or greater than 0 to figure out if your graph will be increasing or decreasing.
Tags: 0, Calculus, decreasing, derivative, function, greater than, increasing, less than, Math, monotonicity, monotonicity theorem, slope, zero
Posted in Calculus | No Comments »
Thursday, September 17th, 2009
Definition of the Mean Value Theorem
Description
A detailed tutorial on the solving of the Mean Value Theorem. Step by step tutorial including several examples of how to solve the Mean Value Theorem for reference.
Overview
You can easily figure out what the Mean Value Theorem is by looking at the word mean – a mean is an average. The Mean Value Theorem states that there is at least one point on the graph of a function where the derivative is equal to the average slope of the entire section of the graph you are looking at. The requirements are that the graph is both continuous and differentiable on the interval [a, b], where a < b. Then there exists some c in (a, b) such that:
f ‘(c) = [f(b) - f(a)] / [b - a]
The Mean Value Theorem is very similar to Rolle’s Theorem, which is a more specific theorem stating the same thing.
Tags: a, average, b, c, Calculus, continuous, derivative, differentiable, interval, Math, mean, mean value theorem, rolle's theorem, slope, theorem, value
Posted in Calculus | No Comments »
Thursday, September 17th, 2009
How to Solve the Equation of a Tangent Line
Description
A detailed tutorial on the solving of the equation of a tangent line. Step by step tutorial including several examples of how to solve the equation of a tangent line for reference.
Overview
A tangent line is the straight line to a curve at any given point that just touches the curve at that point. In a mathematical sense, at that point the tangent line is going in the same direction as the curve. To solve the equation of a tangent line, say that the curve is the graph of the function y = f(x). The point at which the tangent line intersects the curve is p = (a, f(a)). Now, take another point on the curve that is close to the line, which can be expressed as q = (a + h, f(a + h)). The secant line passes through both of these points, and the slope of the secant line is equal to the difference quotient. The difference quotient is expressed as:
Those who have already studied limits will recognize the difference quotient to be the definition of a limit function.
Tags: Calculus, curve, equation, equation of a tangent line, function, graph, limit, line, Math, secant, slope, slope of secant line, tangent
Posted in Calculus | No Comments »
Thursday, September 17th, 2009
Determining the equation of a line
Description
Determining the equation of a line
Overview
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. y=mx+b
Tags: algebra, algebraic equation, applied mathematics, ax+by=c, constant terms, elementary algebra, equation of a line, extrapolation, Geometry, graph, intercept form, interpolation, line graph, linear function, ludwig otto hesse, Math, non-linear equation, parametric form, simultaneous equations, slope, slope intercept, standard form, system of linear equations, two point form, x-coordinate, y=mx+b
Posted in Algebra, Geometry, Math | No Comments »
Tuesday, September 15th, 2009
Finding the Slope of a Line
Description
A detailed tutorial on how to find the slope of a line. Step by step tutorial including several examples of how to find the slope of a line for reference.
Overview
Finding slope isn’t all that difficult. The slope of a line is the numerical expression of the slant of a line on a graph. The slope is represented by the letter m and is written in the format of rise over run – in other words, from point to point, how many spaces up the line goes and how many spaces over. Negative numbers are used if the slope runs either down or to the left instead of up and to the right. If the graph is already provided, the slope can be found by counting. But the correct way to find slope is to use a formula.
m = (change in y) / (change in x)
In order to use this formula, you need to have two points on the line. The change in x is the first x-coordinate minus the second x-coordinate, and the change in y is the first y-coordinate minus the second y-coordinate. The equations in the numerator and denominator are solved seperately and will form one fraction, which will be the slope.
Tags: algebra, change in x, change in y, formula, fraction, graph, graphing, line, m, Math, rise over run, slope, x-coordinate, y-coordinate
Posted in Algebra | 1 Comment »
Monday, September 14th, 2009
The Power of the Point Slope Formula
Description
A detailed tutorial on the usage of the Point Slope Formula. Step by step tutorial including several examples of how to use Point Slope Formula for reference.
Overview
The point slope formula is a notation that gives you all of the information you need to graph a line. It contains the slope as well as the y-intercept. Here is the formula:
The 
variable represents the slope (rate of change), while the 
represents the y-intercept (
value where 
).
Tags: algebra, Geometry, graph, line, linear, Math, point, slope
Posted in Algebra, Geometry, Math | No Comments »
