Question 1: Plot the graph of y=2x+3 on the grid. Confirm the slope and y-intercept from the graph.

Answer: slope = 2, y-intercept = 3

Question 2: Using the graph provided (drawn on the grid), find the coordinates of two points on the line and calculate the slope.

Answer: e.g., (1,5) and (3,1); slope = (1-5)/(3-1) = -2

Question 3: Determine the y-intercept from a line that crosses the y-axis at (0, -4).

Answer: -4

Question 4: Construct the equation of a line passing through (2, 5) with a slope of -1 on the grid.

Answer: y = -1(x - 2) + 5 = -x + 7

Question 5: Identify the slope of the line from the graph shown. The line passes through (0, 2) and (4, -2).

Answer: slope = (-2 - 2)/ (4 - 0) = -1

Question 6: Given a line with equation y = -0.5x + 4, plot this line on the grid. Then, verify the y-intercept from the graph.

Answer: y-intercept at (0,4)

Question 7: Find the equation of a line passing through points (1, 2) and (3, 6).

Answer: slope = (6-2)/(3-1) = 2; y = 2x + 0

Question 8: A line on the graph has a slope of 3 and crosses the y-axis at -2. Write its equation.

Answer: y = 3x - 2

Question 9: Identify an error in this line's equation derived from its graph: y = 0.5x + 5, when the line shown has a y-intercept at 2 and slope 1.

Answer: Error: slope or intercept is incorrect; should be y = 1x + 2

Question 10: Given the line y = -2x + 8, draw it on the grid and find the coordinates of the point where it crosses y = 0.

Answer: 0 = -2x + 8; x=4; crossing at (4, 0)

Question 11: Challenge: The graph shows a line passing through (−1, 3) and (2, -1). Derive its equation in slope-intercept form.

Answer: slope = (-1 - 3)/ (2 - (−1)) = -4/3; y = -4/3 x + b; using point (−1, 3): 3 = (-4/3)(−1) + b; 3 = 4/3 + b; b = 3 - 4/3 = 5/3. Equation: y = -4/3 x + 5/3