Question

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Trend Lines Practice
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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**