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7th Grade Math Explanation/Summary?

Hi, so I'm in 8th grade algebra right now. In 7th grade, I had an incredibly terrible teacher so basically a years worth of knowledge I should have, well, I don't have it. There's a big test coming up and it requires me to know and understand the stuff I never learned in 7th grade. My biggest problem area is graphs, and the equations that go along with them. I simply don't understand how you can identify an entire equation by looking at a graph?

Basically, I just need somebody to explain to me important parts of STEM 7/8 math, especially things having to do with graphs! Or if you can't explain, just list every subject I need to know, please? The best explanation AND summary gets 5 stars. thanks!

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  • 4 years ago
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    It seems you want an entire 7th grade math education in the space of a single Yahoo answer. Even if it could be written, you probably wouldn't read it all. The links point to pages that list the topics covered in STEM 7/8 math (and science and technology and engineering--which is what STEM is about). 7th grade topics are listed about 1/3 of the way down the page at the second link.

    I suggest that a suitable level of detailed instruction can be found on YouTube by searching for videos on one or more of the listed topics. It may take some browsing to find an instructor that has a presentation rate and style compatible with the way you learn. Often, too, you can find worksheets on these topics with a web search, so you can work a variety of problems if you want to.

    As for graphs, there are a few ideas that recur.

    1. Coordinates. A normal graph is two-dimensional. Points on the graph are designated using an "ordered pair" with the independent variable usually listed first. Conventionally, the first of the coordinates is the x-coordinate, and it specifies the distance to the right of some vertical reference line, the line x=0. Likewise, conventionally, the second coordinate is the y-coordinate, which specifies the distance above the horizontal reference line, y=0. The "origin" is the point (0, 0) where the reference lines cross.

    Graphs may use any coordinate system that is convenient for the purpose. The (x, y) coordinates are referred to as "rectangular" coordinates because they are usually plotted on a square or rectangular grid. The axes do not need to be labeled "x" and "y". They could be labeled "years" and "population", for example, or "longitude" and "latitude", or "time" and "distance".

    You will also run across "polar" coordinates, (r, θ). In this case, the first coordinate specifies the distance from the origin, and the second specifies that angle at which that distance is measured. The angle is usually measured counterclockwise from a horizontal line extending to the right of the origin.

    2. Intercepts. A line or a curve plotted on rectangular coordinates (also called Cartesian coordinates) may cross the x=0 line (y-axis) or the y=0 line (x-axis). Any point at which the curve meets or crosses the x-axis is called an x-intercept. Any point at which the curve meets or crosses the y-axis is called the y-intercept. These intercepts are often the solutions to equations, and may be used to write equations that describe the graphed curve.

    The equation of a line, for example, can be written in "intercept form" as

    .. x/(x-intercept) + y/(y-intercept) = 1

    That is, the equation

    .. x/2 + y/3 = 1

    will have an x-intercept of 2 (at coordinate (2, 0)) and a y-intercept of 3 (at coordinate (0, 3)).

    3. Slope. You're probably familiar with the idea of slope as applied to land or roads or parts of buildings (roof, deck, driveway, etc.). A steep slope increases (or decreases) rapidly in height relative to horizontal distance. The slope of a line or curve on a graph is measured or described the same way.

    The numerical value of the slope of a line or curve between two points is the change in vertical (y) dimension divided by the change in horizontal (x) dimension. The slope of a curve is the limit of that ratio as the points become arbitrarily close together. A line that is tangent to a curve will have the same slope that the curve does at the one point where the line and curve meet. (Depending on the curve, a line that is tangent to the curve at one point may intersect the curve again at a different point.)

    The slope of a horizontal line is zero (no vertical change). The slope of a vertical line is "undefined" because the denominator of the slope description is zero, and division by zero generally gives a value that is undefined.

    Above, we gave the "intercept form" version of the equation for a line. There are several other forms that are useful. One of the more common is the "slope-intercept form:"

    .. y = mx + b

    In this form, the coefficient "m" is the slope of the line, and the constant "b" is the y-intercept--the y-value when the x-value is zero. For example, the line given by the equation

    .. y = (-3/2)x + 3

    will graph as the same line as the one whose equation is given in intercept from above.

    Distinct lines with the same slope are parallel. Perpendicular lines will have slopes that are negative reciprocals of one another. For example, the line y = 2/3x -1 will be perpendicular to the lines previously discussed.

    Perhaps this discussion of slope and intercept has shown you how the equation for a line can be determined from the graph. (And, perhaps you can see how to read an equation to find information relevant to creating a graph of it.)

    _____

    Equations from Graphs

    There are a few forms of equations that are generally studied in beginning algebra courses. In general, these are the equations of conic sections: parabola, ellipse, circle, hyperbola. Various forms of these equations can be written based in information that may be found on a graph. Sometimes, a focus and directrix are given. Sometimes a vertex and intercepts are given. Sometimes a center and axes lengths are given. Each set of given information allows you to fill in the constants in the corresponding equation. There are too many variations to describe in detail here. Again, a YouTube or web search will get you any desired level of detailed instruction in this area.

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