https://file.aiquickdraw.com/mathbot/file/1726158343896b3pmjnyn.jpg

To solve this problem, we need to determine the **y-intercept** and **slope** of the linear function from the table of values.

### Step 1: Calculate the Slope
The slope \( m \) of a linear function can be calculated using two points \((x_1, y_1)\) and \((x_2, y_2)\) from the table, using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
We'll pick any two points from the table. Let's use \((-2, -14)\) and \((0, -8)\).

\[
m = \frac{-8 - (-14)}{0 - (-2)} = \frac{-8 + 14}{0 + 2} = \frac{6}{2} = 3
\]
Thus, the slope \( m \) is **3**.

### Step 2: Find the y-intercept
The y-intercept is the value of \( y \) when \( x = 0 \). From the table, we see that when \( x = 0 \), \( y = -8 \). Therefore, the y-intercept is \( -8 \).

### Final Answer:
- **y-intercept**: \(-8\)
- **slope**: \(3\)

Do you want more details or have any questions? Here are five related questions to deepen your understanding:

1. How would the equation of the line look using the slope and y-intercept?
2. What does the slope represent in terms of the linear function?
3. How can you find the slope if you only have one point and the equation of the line?
4. What happens to the graph of the function if the slope is negative?
5. How can you determine if a table of values represents a linear function?

**Tip:** Always double-check the table values by plugging them into the slope formula to ensure accuracy when calculating the slope.

Find the y-intercept and slope of the function's graph given the table of values: x = -2, 0, 2, 4; y = -14, -8, -2, 4.

Learn how to find the y-intercept and slope of a linear function using a table of values. This problem involves key algebraic concepts such as calculating the slope using the formula m = (y2 - y1) / (x2 - x1). 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