Question 1: Write the equation of a line that has a Y-intercept of 5 and passes through the point (2, 9).

Answer: y = 2x + 5

Question 2: Calculate the Y-intercept of the line given by the equation y = -3x + 7.

Answer: 7

Question 3: A shopping cart total is modeled by y = 4x + 10, where x is the number of items. What is the total cost when no items are added?

Answer: 10

Question 4: Construct the line that has a Y-intercept of -2 and passes through the point (3, 4).

Answer: y = 2x - 2

Question 5: If a line has a Y-intercept of 6 and a slope of 0, what does its graph look like?

Answer: A horizontal line crossing the Y-axis at 6

Question 6: A store offers a discount modeled by y = -1.5x + 50, where x is the number of items bought. What is the Y-intercept, and what does it represent in this context?

Answer: 50; the original price when no items are bought

Question 7: Plot the graph of y = 2x on the grid. What is the Y-intercept?

Answer: 0

Question 8: A line models the total cost y for buying x items, with a Y-intercept of 3. Write an example equation for this line with a slope of 5.

Answer: y = 5x + 3

Question 9: Identify the common mistake: A student writes the equation as y = 3x + 7, assuming the Y-intercept is 7, but the point (2, 13) lies on the line. What's wrong?

Answer: They misidentified the Y-intercept; it should be 3 if the line passes through (0, 7), but given the point (2,13), the intercept is actually 7, so their assumption is correct. Alternatively, if the line is y=3x+7, it passes through (0,7). The mistake is assuming the intercept without checking the point.

Question 10: Challenge: A line passes through points (1, 4) and (3, 10). Find its Y-intercept.

Answer: y = 3x + 1