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=
Remaining Attempts : 3
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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:

\[
y = x + 12
\]