Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint. Let y represent the area (in square meters) left to paint after x hours. Which of the following information about the graph of the relationship is given? Choose 1 answer: (A) Slope and x-intercept (B) Slope and y-intercept (c) Slope and a point that is not an intercept (D) x-intercept and y intercept (E) y-intercept and a point that is not an intercept (F) Two points that are not intercepts

Question

Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint. Let  y represent the area (in square meters) left to paint after  x hours. Which of the following information about the graph of the relationship is given? Choose 1 answer: (A) Slope and  x-intercept (B) Slope and  y-intercept (c) Slope and a point that is not an intercept (D)  x-intercept and  y intercept (E)  y-intercept and a point that is not an intercept (F) Two points that are not intercepts

Bytelearn · Accepted Answer

Calculate Initial Area: Determine the initial area left to paint before Hiro starts painting. Hiro has painted for 3 hours at a rate of 8 square meters per hour. To find the initial area, we add the area he has painted to the area left to paint. Calculation: 3 hours * 8 square meters/hour = 24 square meters painted. The area left to paint after 3 hours is 28 square meters, so the initial area is 24 square meters + 28 square meters = 52 square meters.Write Equation Relationship: Write the equation that represents the relationship between the area left to paint (y) and the hours spent painting (x). Since Hiro paints at a constant rate, the slope (m) of the line is the negative of the rate of painting because the area left to paint decreases as time increases. Calculation: Slope (m) = -8 (since the area decreases by 8 square meters per hour). The y-intercept (b) is the initial area left to paint, which we found to be 52 square meters. Equation: y = -8x + 52Identify Given Information: Identify the given information based on the equation. We have the slope of the line, which is -8, and the y-intercept, which is 52. The x-intercept is not given directly, but it could be calculated from the equation if needed. We also have a specific point on the line, which is (3, 28), representing the area left to paint after 3 hours.Match Information to Choices: Match the given information to the answer choices. We have the slope of the line and a specific point that is not an intercept (3, 28). This corresponds to answer choice (C) Slope and a point that is not an intercept.

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