Y-Intercept Answer Key

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📊 Part 1: Identifying Y-Intercepts

1. What is the y-intercept of the line y = x + 3?

Answer: y-intercept = 3 or (0, 3)

Explanation: In the form y = mx + b, the y-intercept is the value of b. When x = 0, y = 0 + 3 = 3.

2. Find the y-intercept of the equation 2x + y = 6.

Answer: y-intercept = 6 or (0, 6)

Explanation: Set x = 0: 2(0) + y = 6, so y = 6. The line crosses the y-axis at point (0, 6).

3. What is the y-intercept of the line passing through points (0, -2) and (3, 1)?

Answer: y-intercept = -2 or (0, -2)

Explanation: The y-intercept occurs when x = 0. Since (0, -2) is given, the y-intercept is -2.

4. For the line y = x - 4, what point does the line cross the y-axis?

Answer: (0, -4)

Explanation: The y-intercept is -4, so the line crosses the y-axis at the point (0, -4).

📈 Part 2: Y-Intercept Effects and Graph Shifts

5. How does changing the y-intercept from 2 to 5 affect the graph of y = x + b?

Answer: The entire line shifts up 3 units vertically.

Explanation: Changing from y = x + 2 to y = x + 5 moves every point on the line up by 3 units. The slope remains the same (m = 1), but the vertical position changes.

6. Predict: If y = x + 1 is shifted down 4 units, what is the new equation?

Answer: y = x - 3

Explanation: Shifting down 4 units means subtracting 4 from the y-intercept: 1 - 4 = -3. The new y-intercept is -3.

7. Compare the vertical positions of these lines: y = x + 2, y = x, and y = x - 1.

Answer: y = x + 2 is highest, y = x is in the middle, y = x - 1 is lowest.

Explanation: All have slope = 1, but different y-intercepts (2, 0, -1). Higher y-intercepts create lines positioned higher on the graph. They are parallel lines with vertical spacing of 1 unit between each.

🎯 Part 3: Application Problems

8. A line has slope 1 and passes through (0, 7). Write the equation and explain what the y-intercept represents.

Equation: y = x + 7

Y-intercept meaning: The y-intercept of 7 represents the starting value when x = 0. It's where the line begins on the y-axis before increasing at a rate of 1 unit up for every 1 unit right.

9. If a line y = x + b passes through the point (2, 5), find the y-intercept.

Answer: y-intercept = 3

Work: Substitute (2, 5) into y = x + b: 5 = 2 + b, so b = 3. The y-intercept is 3.