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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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How to Use the Distance and Midpoint Formulas on a Coordinate Plane

distance and midpoint formula: Diagram using 1-3 and 3-7 points

With the distance and midpoint formulas, you can find the distance and midpoint between any two points on a coordinate plane.

The distance formula gives you the distance d, expressed as a single value, between the two endpoints:

distance and midpoint formula: Distance formula

The midpoint formula gives you the midpoint, expressed as an ordered pair, between the two endpoints:

Midpoint formula

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How Does the Exterior Angle Theorem Work?

exterior angle theorem: Triangle with adjacent angles

Image credit: Desmos

Before we cover the exterior angle theorem, let's review a few definitions.

  • Adjacent angles: angles that share a side and a vertex (ex., BCA and DCA)
  • Supplementary angles: two angles that add to 180°
  • Interior angles: the angles inside a triangle
  • Exterior angles: angles formed between a side of a shape and a line that extends from the next side

We'll use the above triangle to demonstrate the exterior angle theorem's principles:

  1. An exterior angle should equal the sum of the remote interior angles of a triangle. In the triangle above, the exterior angle of the triangle, angle ACD, will equal the sum of the measures of interior angles BAC and ABC.
  2. An exterior angle and its adjacent interior angle are supplementary angles, so they add to 180°. Above, BCA plus ACD add to 180°.
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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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