Question

Vocabulary Terms - Define/Illustrate

Y-intercept from a table
Y-intercept from a graph
Y-intercept from an equation

Answer 1

### Vocabulary Terms - Definitions and Illustrations

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**1. Y-Intercept from a Table**

**Definition:**
The y-intercept is the value of \( y \) when \( x = 0 \). In a table of values, it can be found by locating the row where the \( x \)-value is zero.

**Illustration:**

| \( x \) | \( y \) |
|-----------|-----------|
| -2 | 3 |
| -1 | 2 |
| 0 | 5 | ← Y-intercept
| 1 | 8 |
| 2 | 11 |

From the table above, when \( x = 0 \), \( y = 5 \). Therefore, the y-intercept is \( (0, 5) \).

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**2. Y-Intercept from a Graph**

**Definition:**
The y-intercept on a graph is the point where the line (or curve) crosses the y-axis. It occurs when \( x = 0 \).

**Illustration:**

*(Note: For illustration purposes, this is a placeholder. A proper graph would show a line crossing the y-axis.)*

In the graph above, the line crosses the y-axis at the point \( (0, 4) \), so the y-intercept is \( 4 \).

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**3. Y-Intercept from an Equation**

**Definition:**
To find the y-intercept from an equation, you substitute \( x = 0 \) into the equation and solve for \( y \).

**Illustration:**

Consider the linear equation:

\[
y = 2x + 3
\]

To find the y-intercept:

1. Substitute \( x = 0 \):

\[
y = 2(0) + 3 = 3
\]

2. Therefore, the y-intercept is \( (0, 3) \).

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These three methods provide different approaches to identifying the y-intercept in various contexts: tables, graphs, and equations.