Arithmetic Sequences Practice

Question

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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Answer 1

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.