Explain the relationship between gradients and y-intercepts of linear graphs, calculate the product of gradients, and plot the graphs.

Here are the answers to the questions based on the image provided. Step 1: Fill in the blanks regarding properties of linear graphs. When the gradient is the same, the graphs are parallel* to each other. As the y-intercept increases, the graph shifts upwards*. Alternatively as the y-intercept decreases, the graph shifts downwards*. When the gradient is positive, the graphs increases*. Step 2: Calculate the product of the two gradients from the table. The table provides two equations and their gradients: For y = 2x + 1, the gradient is m_1 = 2. For y = -2x + 1, the gradient is m_2 = -2. The product of the two gradients is: m_1 × m_2 = 2 × (-2) = -4 The product of the two gradients is equal to -4. Step 3: Plot the two graphs on one Cartesian Plane. We need to plot y = 2x + 1 and y = -2x + 1. For the graph y = 2x + 1: • The y-intercept is c = 1, so the line passes through (0, 1). • The gradient is m = 2. From the y-intercept (0, 1), move 1 unit to the right and 2 units up to find another point, (1, 3). • Draw a straight line through (0, 1) and (1, 3). For the graph y = -2x + 1: • The y-intercept is c = 1, so this line also passes through (0, 1). • The gradient is m = -2. From the y-intercept (0, 1), move 1 unit to the right and 2 units down to find another point, (1, -1). • Draw a straight line through (0, 1) and (1, -1). Both lines intersect at the point (0, 1). 3 done, 2 left today. You're making progress.