Trend Line Equations

Trend Line Equations

Lesson

Why we need equation of trend line

While estimating visually with trend lines is helpful, there are also times when the equation of the trend line can be useful, especially when predicting a value that CANNOT be seen on the graph.

Steps to write equations of trend lines

• 1. Choose any two points on the trend line and set up a ratio of

   $\frac{rise}{run}$  to find the SLOPE of the line, or m.

• 2. Look at the y-axis to find the Y-INTERCEPT of the line, or b.

• 3. Write the equation in slope-intercept form: y = mx + b

Let's look at some trend lines

and find their equations!

Let's start with the y-intercept (b)

What is the y-intercept of this trend line?

Now let's find the slope!

By picking "smart points" and using our Rise (red) and our Run (blue) method, we can see that we have a rise of -30 and a run of 20. We can now make the ratio of

 $\frac{rise}{run}=\frac{-30}{20}=\frac{-3}{2}$  

and we have our slope (m).

Slope

 $\frac{-3}{2}$  mean

A decrease of 3 bowls of soup sales if the temperature increased every 2 degree Celsius.

Multiple Choice

If our y-intercept (b) is 90 and our slope (m) is

 $-\frac{3}{2}$  , then the equation for our trend line is ....

•  $y=-90x\ +\ \frac{-3}{2}$  

•  $y\ =\ -\frac{3}{2}x\ +\ 90$  

•  $y\ =\ 90x\ -\frac{3}{2}$  

•  $y\ =\ -\frac{3}{2}x\ -\ 90$  

Your Turn

Try to come up with the equations for the following trend lines.

Open Ended

What is the y-intercept of this line?

Open Ended

What is the lope of this line?

Multiple Choice

What is the equation of the line?

• y = -10x

• y = 10x + 60

• y = 10x

• $y\ =\ \frac{-1}{10}x\$

Multiple Choice

What is the equation for the trend line shown?

• $y\ =\frac{-10}{3}x\$

• $y\ =\ \frac{10}{3}x$

• $y\ =\ \frac{-1}{3}x$

• $y\ =\ \frac{1}{3}x$

Use trend line equation to make predictions

• If they gave you the x value than replace the x in the equation and solve for y.

• If they gave you the y value, than replace the y in the equation and solve for x.

The trend line equation is  $y\ =\ \frac{10}{3}x\$  

• What is the total number of visit if the age is 15 years?

• we replace the x with 15 in the linear equation $y\ =\ \frac{10}{3}\left(15\right)$  

• Solve for y (use desmo) by multiplying 10/3 with 15.

• y = 50

The trend line equation is  $y\ =\ \frac{10}{3}x\$  

• What is the age if the number of visits is 35

• we replace the y with 35 in the linear equation $35\ =\ \frac{10}{3}x$  

• Solve for x (use desmo) :   35 divide by 10/3 

• x = 10.5 years

Multiple Select

Choose the best answer:

If the trend line is y = -2x + 10 and x is 5 what is y?

• Replace x with 5 and solve for y.

• Replace y with 5 and solve for x

Multiple Choice

Choose the best answer:

If the trend line is y = -2x + 10 and x is 5 what is y?

• x = 2.5

• y = 0

• y = 20

Multiple Choice

Look at the graph, what is the y-intercept (b)?

• 0

• 9

• 120

Multiple Choice

Look at the graph, what is the slope (m)?

•  $\frac{10}{3}$  
  

•  $\frac{-10}{3}$  
  

•  $\frac{1}{6}$  
  

•  $\frac{-1}{6}$  

Multiple Choice

Given the equation for the graph, what does the slope respresent?

 $y\ =\ \frac{-10}{3}x\ +\ 120$  

• a decrease of 120 towels per roll for every 10 years

• an increase of 10 towels per roll for every 3 years

• a decrease of 10 towels per roll for every 3 years

Multiple Choice

Given the equation for the graph, how many paper towels are in a roll in 12 years?

 $y\ =\ \frac{-10}{3}x\ +\ 120$  

• 40

• 80

• 30

OK let's see what you remember!

Multiple Choice

What is the type of correlation for the following scatter plot?

• Negative

• Positive

• No Correlation

Multiple Choice

What type of association does this graph have?

• positive

• negative

• None

• all of the above

Multiple Choice

Write the equation for the trend line.

• y = 0.5x

• y = -0.5x

• y = 2x

• y = -2x

Multiple Choice

What is a line of best fit used for?

• To make predictions

• To connect the points

• To make the graph look pretty

Multiple Choice

What is the equation for the trend line shown?

• $y\ =-\ \frac{2}{3}x\ +\ 40$

• $y\ =\ \frac{2}{3}x$

• $y\ =\ 40x$

• $y\ =\ \frac{20}{3}x\ +40$

Multiple Choice

What kind of correlation does this graph have?

• positive

• negative

• no correlation

Multiple Choice

The equation of the graph is  $y\ =\ \frac{20}{3}x\ +\ 40$  , if x is 15 what is y?

• 100

• 140

• 60

• 40

Multiple Choice

If a scatterplot has no correlation then....

• ...it has no ordered pairs

• ...its ordered pairs have no predictable pattern

• ...it has ordered pairs that have a negative pattern

• ..if it makes a bear on a graph

Multiple Choice

The slope is -5/7, what does that mean?

• gain 5 hour of sleep for 7 cups of coffee

• lose 7 cups of coffee for 5 hours of sleep

• lose 5 hours of sleep for 7 cups of coffee

• lose 5 cups of coffee for 7 hours of sleep

Multiple Choice

Which line represent the best trend line or line of best fit?

• A

• B

• C

• all of them

Multiple Choice

What is the correlation between the data?

• positive correlation

• negative correlation

• no correlation