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How to Identify the Constant of Proportionality

constant of proportionality: graph

Image credit: Desmos

The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship. Other names for the constant of proportionality include the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

In this article, we’ll show you how to find the constant of proportionality and graph its equation through reviewing a sample word problem.

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How to Find the Line of Best Fit in 3 Steps

how to find line of best fit: graph

Imagine you are at a new marketing job. You have a set of data in Excel in front of you about sales numbers, and a scatter plot of those data points in a graphing calculator on your desk. Your boss comes by and asks you to give a regression analysis of the data by noon — he needs to know the trend line of the sales. You rack your brain for how to find the line of best fit, remembering that it involves something with finding a straight line on a scatter plot. What do you do?

The least squares regression is a simple linear regression analysis that is used to find the slope of the line that best fits or represents a set of data points.

A linear equation represents the linear relationship between the x-values and y-values of the points on a graph or chart.

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How to Go From Standard Form Equations to Slope-Intercept Form

standard form equation: man writing on the blackboard

The standard form equation is a linear equation that contains two variables, usually (but not limited) to x-terms and y-terms, that are on the same sides of the equation: Ax + By = C

Coefficients A, B, and C must be whole number integers that have no decimals or fractions. In the standard form equation, coefficients B and C can be positive or negative numbers, but coefficient A must be a positive number.

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The Formula for the Area of Equilateral Triangles

area of equilateral triangle: colorful equilateral triangle

Image credit: Desmos

Before we begin, let’s review what an equilateral triangle is — a triangle with three equal side lengths and three equal internal angles of 60° each. Now, let’s get one thing straight: The area of an equilateral triangle is not the perimeter of an equilateral triangle. It's the total space of the triangle’s surface.

As you know, there are many different types of triangles: right triangles, scalene triangles, and isosceles triangles. Again, in an equilateral triangle, the length of the sides of an equilateral triangle are equal.

To determine the area of an equilateral triangle, you must know its side lengths. So, before diving into the equilateral triangle area formula, let's look at how to find the side lengths.

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Which Angles Relate to Parallel Lines and Transversals?

parallel lines and transversals: vertical angles

Image credit: Desmos

Parallel lines and transversals are two important geometry concepts because they result in special angle relationships you’ll find in different postulates and theorems and use for solving geometry proofs.

First, two definitions:

Parallel lines: Never intersect, or cross, one another

Transversal line: Intersects two or more lines or line segments

When a transversal line crosses a pair of parallel lines, many types of angles can be created. Let’s go over the many different pairs of angles created by parallel lines and transversals:

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