Question 1: Given the equation y = 3x + 7, state the Y-intercept and explain how you identified it.

Answer: The Y-intercept is 7, found by setting x=0 in the equation.

Question 2: Construct the graph of y = -2x + 4 and label the Y-intercept on the grid.

Answer: Y-intercept at 4

Question 3: A line passes through (0, -5) and (2, 1). Write its equation in slope-intercept form and identify the Y-intercept.

Answer: y = 3x - 5; Y-intercept is -5.

Question 4: A student claims that the Y-intercept is always the constant term in the equation. Is this correct? Explain briefly.

Answer: No, because the Y-intercept is the point where the line crosses the Y-axis, found by x=0, which corresponds to the constant term in y=mx + c.

Question 5: Identify the mistake in the following statement: 'The Y-intercept of y = 5x + 2 is 2, so the graph crosses the Y-axis at 2.'

Answer: This is correct; the Y-intercept is at 2.

Question 6: Given the equation y = 2x - 3, find the Y-intercept and verify by substituting x=0.

Answer: Y-intercept at -3; verify: y=2(0)-3 = -3.

Question 7: A line with a Y-intercept at 0 passes through (4, y). Find y and write the equation if the slope is -1/2.

Answer: y = -1/2 * 4 + 0 = -2; Equation: y = -1/2 x.

Question 8: A line's equation is y = -4x + c. If the Y-intercept is at 6, find the value of c.

Answer: c = 6

Question 9: Plot the graph of y = 1/2 x - 3 and identify the Y-intercept on the grid.

Answer: Y-intercept at -3

Question 10: Explain why the Y-intercept is important in understanding the graph of a line.

Answer: It indicates where the line crosses the Y-axis, giving a starting point for graphing and understanding the line's position.

Question 11: Identify and correct the error: 'For the equation y=4x + 9, the Y-intercept is 4.'

Answer: Incorrect; Y-intercept is 9, not 4.

Question 12: A line has a Y-intercept at -2 and slope 3. Write its equation and plot it on the grid.

Answer: y = 3x - 2