Question
Arithmetic Sequences Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
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Question
Use the image to answer the question.
Three points are plotted on a coordinate plane, and a line is graphed through them. The x-axis ranges from negative 5 to 5 in increments of 5. The y-axis ranges from 0 to 30 in increments of 5.
Write the function of the graphed arithmetic sequence.
(1 point)
The function of the arithmetic sequence is
Remaining Attempts : 3
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Answers
Answered by
GPT-4o mini
To determine the function of the arithmetic sequence represented by the line passing through the three plotted points, we need to establish the slope \( m \) and the y-intercept \( b \) of the line in the slope-intercept form \( y = mx + b \).
Here's how you can do that:
1. **Identify the Points**: Check the coordinates of the three plotted points on the graph. We'll denote them as \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \).
2. **Calculate the Slope**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
You can calculate the slope between any two points; choose points that are easy to work with.
3. **Find the Y-Intercept**: After finding the slope, use one of the points to find the y-intercept. Rearranging the equation gives:
\[
b = y - mx
\]
4. **Write the Function**: Now that you have both \( m \) and \( b \), you can write the function of the arithmetic sequence.
If you can provide the specific coordinates of the plotted points, I can help you calculate the exact function. If you don’t have the coordinates, just follow the steps above using the coordinates from the image you're referring to.
Here's how you can do that:
1. **Identify the Points**: Check the coordinates of the three plotted points on the graph. We'll denote them as \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \).
2. **Calculate the Slope**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
You can calculate the slope between any two points; choose points that are easy to work with.
3. **Find the Y-Intercept**: After finding the slope, use one of the points to find the y-intercept. Rearranging the equation gives:
\[
b = y - mx
\]
4. **Write the Function**: Now that you have both \( m \) and \( b \), you can write the function of the arithmetic sequence.
If you can provide the specific coordinates of the plotted points, I can help you calculate the exact function. If you don’t have the coordinates, just follow the steps above using the coordinates from the image you're referring to.