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GMAT Prep: Help and Review25 chapters | 288 lessons | 15 flashcard sets

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

What is a trend line and how is it useful? That's what you'll learn, as well as the formulas you need to use and the numbers you need to find for the equation of a trend line, in this lesson. You'll also see what steps you need to take to manipulate the formulas to your desired equation.

In this lesson, we'll talk about finding the **equation of a trend line**. In the real world, your data will usually be scattered like in this graph instead of lining up neatly in a straight line.

In some real world cases, though, your data will look like it follows a line. If it does, then you'll be able to approximate your data with a line and a linear equation. This line that you approximate your data with is called the **trend line**. If this line is a straight line, then you'll be able to find an equation for this line.

In this lesson, we'll talk about finding an equation for trend lines that are straight lines. For these types of trend lines, you'll be able to find an equation in the slope-intercept form where *m* is your slope and *b* is your *y*-intercept. Remember, your **slope** is how steep your line is. A flat, horizontal line has a slope of 0. A diagonal line on the graph has a slope of 1. Steeper lines have larger slopes. Your ** y-intercept** is where your line crosses the

To find your equation of a trend line, follow these steps.

You begin by drawing your trend line. You want your trend line to follow your data. You want to have roughly half your data above the line and the other half below the line, like this:

Your next step is to locate two points on the trend line. Look carefully at your trend line and look for two easy to figure out points on the line. Ideally, these are points where the trend line crosses a clearly identifiable location.

For the trend line that we just drew, we can see these two easily identifiable points.

We can easily identify these two points as (3, 3) and (12, 6).

The formula for slope is this one:

We can label our first point as (*x*1,*y*1), and our second point as (*x*2,*y*2). So our *x*1 is 3, our *y*1 is 3, our *x*2 is 12, and our *y*2 is 6. Plugging these values into the equation for slope and evaluating, we get this:

So our slope is 1/3.

Your last step uses the point with the smaller numbers to help you find the equation of your trend line. You'll want to use the smaller point as using smaller numbers is easier to work with. You'll be plugging the values of this point into the point-slope formula for the equation of a line to find the equation of your trend line. Your point will be labeled like before as (*x*1,*y*1). The point-slope formula is this one:

You can see that it also uses the slope. You'll plug in your *x*1 and *y*1 along with the slope into the formula. Then you'll evaluate and rewrite it in the slope-intercept form by solving for the *y* variable.

So for our trend line equation, plugging our values of 3 for *x*1, 3 for *y*1, and 1/3 for *m* into the point-slope formula and then solving for *y*, we get this:

From this, we see that our equation for the trend line is *y* = (1/3)*x* + 2, and we are done!

Let's try another example.

Find the equation for this trend line:

To calculate our equation, we first need to locate two points on the trend line.

Looking carefully at this graph, we see that this trend line passes through the points (3, 3) and (5, 7).

We can label these two points with their appropriate *x*1, *y*1, *x*2, and *y*2 labels. Our *x*1 is 3, our *y*1 is 3, our *x*2 is 5, and our *y*2 is 7. Plugging these numbers into the formula for the slope, we find the slope to be this one:

Now, using this slope and the point with the smallest numbers, the (3, 3), we can use the other formula to find our equation:

And we are done! Our equation for this trend line is *y* = 2*x* - 3.

To recap, you can find the equation for trend lines that are straight lines by finding an equation in slope-intercept form where *m* is your slope and *b* is your *y*-intercept. You'll first draw your trend line; then locate two points on the line; then plug those two points into the formula for slope; and then plug the values of the smaller point and the slope into the point-slope formula.

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GMAT Prep: Help and Review25 chapters | 288 lessons | 15 flashcard sets

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