Vocabulary Terms - Definitions and Illustrations
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 \( (0, 5) \).
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 \( 4 \).
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:
- Substitute \( x = 0 \):
\[ y = 2(0) + 3 = 3 \]
- Therefore, the y-intercept is \( (0, 3) \).
These three methods provide different approaches to identifying the y-intercept in various contexts: tables, graphs, and equations.
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