The table represents some points on the graph of a linear function.



Which function represents this relationship?

A

y=−3/2x+4

B

y=−3/2x−14

C

y=−2/3x−9

D

y=−2/3x−1*y*

To find the correct linear function that represents the relationship from a given table of points, we need to determine the slope (\(m\)) and the y-intercept (\(b\)) of the linear equation in the form \(y = mx + b\).

### Steps:
1. **Find the slope \(m\):** The slope can be calculated using any two points \((x_1, y_1)\) and \((x_2, y_2)\) from the table using the formula:

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

2. **Determine the y-intercept \(b\):** After finding the slope, substitute one point \((x, y)\) into the equation \(y = mx + b\) and solve for \(b\).

If you have the points from the table, please share them, and I can proceed with the calculations.

Do you have any questions about this process or want further details?

Here are 5 related questions to consider:
1. How can you determine if a function is linear by looking at a table of values?
2. What is the significance of the slope in a linear function?
3. How do you interpret the y-intercept in the context of a word problem?
4. Can you determine the equation of a line if only given its graph?
5. How would you solve for \(x\) given a specific \(y\)-value in a linear function?

**Tip:** Always check for consistent differences between y-values to confirm a linear relationship when given a table of points.

The table represents some points on the graph of a linear function. Which function represents this relationship?
A. y = −3/2x + 4
B. y = −3/2x − 14
C. y = −2/3x − 9
D. y = −2/3x − 1

Learn how to determine the correct linear function that represents a relationship from a table of points. This problem involves calculating the slope and identifying the y-intercept in the equation y = mx + b. Ideal for students in Grades 8-10.

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