📚 Part 1: Understanding Y-Intercept

What is the Y-Intercept?

The y-intercept is the point where a line crosses the _______ axis. It occurs when x = _____.

Example Equation: y = x + 3

In this equation, the slope is _____ and the y-intercept is _____.

✏️ Part 2: Y-Intercept and Graph Position

How Y-Intercept Affects the Graph:

The y-intercept determines the _____________ position where the line starts on the y-axis.

• y = x + 1 (y-intercept: ____)

• y = x + 3 (y-intercept: ____)

• y = x + 5 (y-intercept: ____)

🎯 Part 3: Practice and Application

a) y = x + 7 Y-intercept: _______

b) y = x - 4 Y-intercept: _______

c) y = x Y-intercept: _______

Equation: y = _____________

📝 Answer Key with Explanations

Part 1 Answers:

• The y-intercept is the point where a line crosses the y axis. It occurs when x = 0.

• In y = x + 3, the slope is 1 and the y-intercept is 3.

1. Answer: b - In y = mx + b, the letter 'b' represents the y-intercept.

2. Answer: (0, 3) - The y-intercept is always written as a coordinate point where x = 0.

Part 2 Answers:

• The y-intercept determines the vertical position where the line starts on the y-axis.

3. y = x + 1 (y-intercept: 1), y = x + 3 (y-intercept: 3), y = x + 5 (y-intercept: 5)

Explanation: As the y-intercept increases, the entire line shifts upward. All three lines are parallel (same slope of 1) but positioned at different heights on the graph.

4. Answer: (0, -2) - The line crosses the y-axis at the point (0, -2), which is 2 units below the origin.

5. Answer: True - A larger y-intercept value moves the line higher on the graph because it increases the starting point on the y-axis.

Part 3 Answers:

6. a) Y-intercept: 7 b) Y-intercept: -4 c) Y-intercept: 0

Note: When there's no constant term (like in y = x), the y-intercept is 0, meaning the line passes through the origin.

7. Sample answer: Changing the y-intercept shifts the line vertically up or down without changing its steepness. A positive y-intercept moves the line above the origin, while a negative y-intercept moves it below the origin.

8. Equation: y = x + 6

Explanation: Since the slope is 1 and we want the line to pass through (0, 6), we use the form y = mx + b where m = 1 and b = 6.