Real math help.
What Does Direct Variation Look Like on a Graph?
Note:
Want to know what a direct variation looks like graphically? Basically, it's a straight line that goes through the origin. To get a better picture, check out this tutorial!
Background Tutorials
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Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
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What is the Origin?
The coordinate plane has two axes: the horizontal and vertical axes. These two axes intersect one another at a point called the origin. Learn about the ordered pair that indicates the origin and its location in the coordinate plane by watching this tutorial!
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What is the Coordinate Plane?
You can't graph a function or plot ordered pairs without a coordinate plane! Learn about the coordinate plane by watching this tutorial.
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Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
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What's the Constant of Variation?
The constant of variation is the number that relates two variables that are directly proportional or inversely proportional to one another. But why is it called the constant of variation? This tutorial answers that question, so take a look!
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What's the Direct Variation or Direct Proportionality Formula?
Ever heard of two things being directly proportional? Well, a good example is speed and distance. The bigger your speed, the farther you'll go over a given time period. So as one variable goes up, the other goes up too, and that's the idea of direct proportionality. But you can express direct proportionality using equations, and that's an important thing to do in algebra. See how to do that in the tutorial!
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Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
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What Does the Slope of a Line Mean?
You can't learn about linear equations without learning about slope. The slope of a line is the steepness of the line. There are many ways to think about slope. Slope is the rise over the run, the change in 'y' over the change in 'x', or the gradient of a line. Check out this tutorial to learn about slope!
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Graph linear and quadratic functions and show intercepts, maxima, and minima.
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What's the Y-Intercept?
When you have a linear equation, the y-intercept is the point where the graph of the line crosses the y-axis. In this tutorial, learn about the y-intercept. Check it out!
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Further Exploration
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Represent proportional relationships by equations.
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How Do You Write an Equation for Direct Variation from a Table?
Looking for some practice with direct variation? Watch this tutorial, and get that practice! This tutorial shows you how to take a table of values and describe the relation using a direct variation equation.
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How Do You Use the Formula for Direct Variation?
If two things are directly proportional, you can bet that you'll need to use the formula for direct variation to solve! In this tutorial, you'll see how to use the formula for direct variation to find the constant of variation and then solve for your answer.
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Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
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How Do You Solve a Word Problem Using the Direct Variation Formula?
Word problems allow you to see math in action! Take a look at this word problem involving an object's weight on Earth compared to its weight on the Moon. See how the formula for direct variation plays an important role in finding the solution. Then use that formula to see how much you would weigh on the Moon!
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