ID Valerie is comparing the costs of block and shredded cheeses.The cost of 8 ounces of shredded cheese is 3.00 Part A The cost of block cheese is shown in the graph. Graph the line that models the cost of shredded cheese in the graph below. Part B Write an equation for the line representing the cost of the shredded cheese. __ Part C Valerie purchases 16 ounces of the less expensive cheese How much does she pay for the cheese?

Part A: Graph the line that models the cost of shredded cheeseTo graph the line that models the cost of shredded cheese, we need to plot the given point (8, 3) on the graph and draw a line through it that starts from the origin (0, 0), since the cost is $0 when 0 ounces of cheese are purchased.Since we don't have an actual graph to draw on, I'll describe how you would do it:1. Plot the point (8, 3) on the graph.2. Draw a straight line through (0, 0) and (8, 3).This line represents the cost of shredded cheese as a function of the amount of cheese in ounces.Part B: Write an equation for the line representing the cost of shredded cheeseTo write the equation of a line, we need two things: a point on the line and the slope. We have the point (8, 3), and we can calculate the slope using the formula:\[ \text{Slope} = \frac{\text{Change in y}}{\text{Change in x}} \]We know that the line passes through (0, 0) and (8, 3), so:\[ \text{Slope} = \frac{3 - 0}{8 - 0} = \frac{3}{8} \]Now, we can use the point-slope form of the equation of a line, which is:\[ y - y_1 = m(x - x_1) \]Where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope. Using the point (8, 3) and the slope \( \frac{3}{8} \), the equation is:\[ y - 3 = \frac{3}{8}(x - 8) \]To simplify and write it in slope-intercept form (y = mx + b), we distribute the slope and solve for y:\[ y - 3 = \frac{3}{8}x - \frac{3}{8} \times 8 \]\[ y - 3 = \frac{3}{8}x - 3 \]\[ y = \frac{3}{8}x \]So, the equation for the line representing the cost of shredded cheese is:\[ y = \frac{3}{8}x \]Part C: Valerie purchases 16 ounces of the less expensive cheese. How much does she pay for the cheese?To determine which cheese is less expensive, we need to compare the cost of 16 ounces of block cheese to the cost of 16 ounces of shredded cheese.For block cheese, we use the graph's line equation. The graph shows a line passing through (0,0) and (20,7), so we can calculate the slope of this line:\[ \text{Slope (block cheese)} = \frac{7 - 0}{20 - 0} = \frac{7}{20} \]The equation for the block cheese line is:\[ y = \frac{7}{20}x \]Now, let's calculate the cost for 16 ounces of block cheese:\[ y = \frac{7}{20} \times 16 \]\[ y = \frac{7}{20} \times \frac{16}{1} \]\[ y = \frac{7 \times 16}{20} \]\[ y = \frac{112}{20} \]\[ y = 5.6 \]So, 16 ounces of block cheese costs $5.60.Now, let's calculate the cost for 16 ounces of shredded cheese using its equation:\[ y = \frac{3}{8} \times 16 \]\[ y = \frac{3}{8} \times \frac{16}{1} \]\[ y = \frac{3 \times 16}{8} \]\[ y = \frac{48}{8} \]\[ y = 6 \]So, 16 ounces of shredded cheese costs $6.00.Comparing the two costs, block cheese is less expensive at $5.60 for 16 ounces compared to shredded cheese at $6.00 for 16 ounces.Therefore, Valerie pays $5.60 for 16 ounces of the less expensive cheese, which is the block cheese.