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A detailed tutorial of the x axis and the  y axis. Step by step tutorial including several examples of the x axis and the y axis for reference.

The the Cartesian coordinate system, there is an x axis and a y axis. The x axis runs horizontally across the system and all first terms in ordered pairs are x coordinates, from the x axis. The y axis runs vertically across the system and all second terms in ordered pairs are y coordinates, from the y axis. The x and y axis work together to use a pattern of right angles and perpendicular lines in order to find ordered pairs and coordinates of x and y on the graph.

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Description

A detailed tutorial on the translation of graphs. Step by step tutorial including several examples of translating graphs for reference.

Overview

There are different ways to translate graphs, but the easiest way is to memorize the general rules for translation. This tells you what parts of the equation do what to your basic graph. Starting with a graph of y = f(x), these would be your basic rules:

y = f(x – a) moves a units to the right

y = f(x + a) moves a units to the left

y = f(x) + a moves a units up

y = f(x) – a moves a units down

y = f(-x) reflects over the y-axis

y = -f(x) reflects over the x-axis

Reflections are always done before translations, not the other way around, because if you do your translation first you will end up with your shape having the wrong coordinates.

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Description

A detailed tutorial on how to use the Vertical Line Test for grphing functions. Step by step tutorial including several examples of how to use the Vertical Line Test for reference.

Overview

The Vertical Line Test is a test used to find out if a graph is a function or not. If the vertical line only passes through the line or curve once, then the graph is a function. If the vertical line passes through the line or curve more than once, or not at all, then the graph is not a function. The vertical line only hitting the graph once must be true for every single place the vertical line could be drawn or the graph is not a function.

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Description

This video is a tutorial on how to find x and y intercepts when graphing an equation. It is shown how to continue on and graph the problem. This video provides several example problems.

Overview

Finding x and y intercepts is a simple process if the graph is in front of you, but what if you need to find the intercepts in order to graph the equation? An x-intercept is the point where the line or curve intercepts the x-axis, and is expressed as (x,0). A y-intercept is the point where the line or curve intercepts the y-axis, and is expressed as (0,y). Because you know that when you are solving for an intercept, the other variable is 0, this makes it quite easy to solve for. In a normal graphing equation, there are two variables, an x and a y. To solve for an x-intercept, set the y value equal to 0 and solve for x. To solve for a y-intercept, set the x value to 0 and solve for y. These are your intercepts.

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Description

This video outlines the different parts of the graphs and illustrates how to properly label all parts of the coordinate plane. Real world examples are given of graphs and graphing systems. Examples of how to plot points are provided in the video.

Overview

The coordinate plane, or the cartesian plane, is commonly known by math students as a blank graph. Graphs consist of two lines that are perpendicular to each other – the horizontal x axis and the vertical y axis. Each axis has a set of numbers, where the top and right of the lines are positive and the bottom and left of the lines are negative. The very center of the graph is known as the origin. The origin is the point (0, 0). Because of the two lines, the graph is split up into 4 sections, called quadrants. The quadrants are labelled at I, II, III, and IV (roman numerals for 1, 2, 3, and 4). They start at the top right corner and continue counter-clockwise around the graph. Quadrant I is a positive quadrant, Quadrant III is a negative quadrant, and Quadrants II and IV have both positive and negative numbers. Points on the graph are found in these four quadrants. The points are written as (x, y) and can be found by tracing up and down along the number values on the graphs until the two lines meet. The place where the lines meet is your point.

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Description

This video gives one example of how to use the midpoint formula when given two (x, y) points. Tips for solving are included in the video. This video provides a more complicated example to show that midpoint is not impossible to find when given more complicated numbers.

Overview

The midpoint formula is similar to the distance formula because it used for lines and graphs. Very often the two formulas are used together. The midpoint formula is not so much a formula as a point on the line that you must solve for. The formula is ({x1 + x2}/2 , {y1 + y2}/2). In order to use this formula, you must be given two points on a graph: (x1, y1) and (x2, y2). Plug these in their proper place in the formula and solve the equations. You should end up with another (x, y) point. This is your midpoint – the point right in the middle of these two points you were given.

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Description

This video gives very clear examples and explanations on how to find the mean, median, and mode in a set of numbers, using both number sets and graphs to illustrate how to find the mean, median, and mode. Both examples for basic arithmetic uses and complicated statistics uses are given, as well as examples of tools that can be used to help solve these problems.

Overview

The mean, median, and mode are sometimes known as the average, the middle, and the most. The mean is the average of a set of numbers. To find the average, you need to add up all the numbers in the set and then divide the sum by how many numbers there are. For example, take the set 1, 2, 3. 1 + 2 + 3 = 6. Then divide 6 by 3, as that is how many numbers there are. The mean is 2. The median is the middle of a set of numbers. The easiest way is to set up all the numbers in value of lowest to highest, and cross off numbers on each end until you are left with one in the middle. In the event that you are left with two numbers in the middle, you need to take the mean of those two numbers. For example, the set 1, 2, 3, 4. The two middle numbers are 2 and 3. 2 + 3 = 5. The median would be 5/2, or you can put that in decimal form. The mode is the number that occurs the most. You may have more than one number for the mode. You may also have no mode. In the set 1, 2, 2, 2, 2, 3, 3, 4, 5, 5, 5, 6, 6, 6, 6, the mode is both 2 and 6 because those numbers occur the most in the set. Mean, median, and mode are most commonly used in data sets and statistics.

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Description

This video shows how to solve one distance formula problem, with a “solve it yourself” option available. It provides a clear method of solving and easy explanations. The steps are laid out in an easy to follow method.

Overview

Distance is a very common formula in geometry. The formula that is used to solve distance is d = sqrt[(x2 - x1)^2 - (y2 - y1)^2]. In order to use the distance formula, you must be given two points on a graph, represented as (x1, y1) and (x2, y2). You then must plug them in the appropriate places on the distance formula. Continue to solve as you would any basic algebra problem, using the order of operations.

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Description

This video explains how to solve equations and put them into the format y = mx + b so they can easily be graphed. It provides two examples of slightly different equations and shows how to put them into a slope-intercept form so you can graph the equations.

Overview

When graphing, you may be asked to graph an equation that looks like x + y = b. In order to graph this equation, it needs to be in the form of y = mx + b. This is called slope-intercept form. The slope of the line is represented by m, in the form of rise over run, and the y-intercept is represented by b. As in normal algebra problems, you will be required to add, subtract, or divide as neccessary to place the numbers and variables in their proper place.