Question 1: Given the equation y = 3x + 5, identify the y-intercept and explain how you determined it.

Answer: The y-intercept is 5, because it is the constant term when the equation is in slope-intercept form y = mx + b.

Question 2: Rewrite the equation 2x - y = 4 in slope-intercept form and state its y-intercept.

Answer: y = 2x - 4; y-intercept is -4

Question 3: Plot the graph of y = -x + 2 on the grid. What is the y-intercept?

Answer: 2

Question 4: Construct the equation of a line with a y-intercept of 7 and slope 4. Write the equation in slope-intercept form.

Answer: y = 4x + 7

Question 5: If a line passes through point (2, 3) and has a y-intercept of -2, derive its equation.

Answer: y = m x - 2; m = (3 - (-2)) / (2 - 0) = 5/2; Equation: y = (5/2)x - 2

Question 6: Identify the mistake in the following equation: y = 4x + 3, but the student claims its y-intercept is 4.

Answer: The y-intercept is 3, not 4, because in y = mx + b, b represents the y-intercept.

Question 7: Find the equation of a line with a y-intercept of -5 that passes through (4, 3).

Answer: slope m = (3 - (-5)) / (4 - 0) = 8/4 = 2; Equation: y = 2x - 5

Question 8: A line has the equation y = -1/2 x + 6. What is its y-intercept and how do you know?

Answer: The y-intercept is 6, as indicated by the constant term in the equation.

Question 9: Derive the equation of a line with y-intercept 0 and slope -3, passing through (5, -15).

Answer: Equation: y = -3x

Question 10: Explain why the equation y = 7 is a horizontal line and what is its y-intercept?

Answer: It's a horizontal line because y remains constant at 7 for all x-values; y-intercept is 7.

Question 11: Given the equation y = 2x + 3, find the y-intercept and demonstrate how changing the constant term affects the y-intercept.

Answer: Y-intercept is the constant term (3). Increasing or decreasing this value shifts the line vertically without changing slope.

Question 12: A student makes the mistake of stating that the y-intercept of y = -x + 4 is 0. Identify and correct this mistake.

Answer: The y-intercept is 4, not 0, because it is the constant term in the equation y = -x + 4.