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Question

Trend Lines Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items

Question
Use the image to answer the question.

An illustration of a scatterplot graph shows x-axis ranging from 0 to 10 in increments of 1 and y-axis ranging from 0 to 30 in increments of 2. Multiple points are plotted around a line that points upward to the right with an arrowhead on the bottom.
The line passes approximately through left parenthesis 0 comma 12 right parenthesis, left parenthesis 4 comma 16 right parenthesis, and left parenthesis 6 comma 18 right parenthesis. 12 points are plotted close to the line.

Write an equation in slope-intercept form of the trend line.

(1 point)
y=
+

Answer 1

To find the equation of the trend line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).

From the given points on the trend line, we can use two of them to calculate the slope. Let's use the points (4, 16) and (6, 18).

1. Calculate the slope (m):

The formula for slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points \( (4, 16) \) and \( (6, 18) \):

• \( x_1 = 4, y_1 = 16 \)
• \( x_2 = 6, y_2 = 18 \)

\[ m = \frac{18 - 16}{6 - 4} = \frac{2}{2} = 1 \]

2. Find the y-intercept (b):

To find b, we can use one of the points and the slope in the equation \( y = mx + b \). Let's use the point \( (4, 16) \):

\[ 16 = 1(4) + b \]

This simplifies to:

\[ 16 = 4 + b \] \[ b = 16 - 4 \] \[ b = 12 \]

3. Write the equation:

Now that we have the slope \( m = 1 \) and the y-intercept \( b = 12 \), we can write the equation in slope-intercept form:

\[ y = 1x + 12 \]

or simply:

\[ y = x + 12 \]

Thus, the final answer is:

y = x + 12