Use the image to answer the question.

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=
Remaining Attempts : 3
Skip to navigation

Answer 1

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

From the points provided that the trend line passes through:

• Left parenthesis \( (0, 12) \)
• Left parenthesis \( (4, 16) \)
• Left parenthesis \( (6, 18) \)

Step 1: Calculate the Slope \( m \)

The slope \( m \) is calculated using the formula:

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

Using the points \( (4, 16) \) and \( (0, 12) \):

\[ m = \frac{16 - 12}{4 - 0} = \frac{4}{4} = 1 \]

Step 2: Determine the Y-Intercept \( b \)

The y-intercept \( b \) can be found from the point \( (0, 12) \). When \( x = 0 \), \( y = b \).

So, from the point:

\[ b = 12 \]

Step 3: Write the Equation

Now we can write the equation of the trend line in slope-intercept form:

\[ y = mx + b \]

Substituting the values of \( m \) and \( b \):

\[ y = 1x + 12 \]

Thus, the equation of the trend line is:

\[ y = x + 12 \]