https://file.aiquickdraw.com/mathbot/file/17283333987500eskptbn.jpg

Let's first find the **slope** and **y-intercept** of the linear relationship shown in the table.

The formula for the slope (\(m\)) of a line is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's use the two points \((5, 16.5)\) and \((7, 21.5)\) from the table:
\[
m = \frac{21.5 - 16.5}{7 - 5} = \frac{5}{2} = 2.5
\]

So, the slope (\(m\)) is **2.5**.

Now, we use the slope-intercept form of the equation of a line, \(y = mx + b\), to find the **y-intercept** (\(b\)).

We already know that \(m = 2.5\). Using one of the points, say \((5, 16.5)\):
\[
y = mx + b
\]
\[
16.5 = 2.5(5) + b
\]
\[
16.5 = 12.5 + b
\]
\[
b = 16.5 - 12.5 = 4
\]

Thus, the **y-intercept** is **4**.

### Summary:
- The slope is **2.5**.
- The y-intercept is **4**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the slope change if the difference between the y-values increased?
2. Can you use the equation of the line to predict the value of \(y\) when \(x = 10\)?
3. How would the graph of the line look based on the slope and y-intercept?
4. What is the interpretation of the slope in real-world scenarios?
5. How can you find the slope from any two points on a line?

**Tip:** The slope tells you how much \(y\) changes for each unit increase in \(x\).

The table shows a linear relationship between the variables x and y. What are the slope and the y-intercept of the linear relationship? The table includes the points (5, 16.5), (7, 21.5), and (11, 31.5).

Learn how to find the slope and y-intercept from a table of values that shows a linear relationship between x and y. This problem covers core algebra concepts, including the slope formula and the slope-intercept form of a line. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation