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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

Hiro painted his room. After 33 hours of painting at a rate of 88 square meters per hour, he had 2828 square meters left to paint.\newlineLet y y represent the area (in square meters) left to paint after x x hours.\newlineWhich of the following information about the graph of the relationship is given?\newlineChoose 11 answer:\newline(A) Slope and x x -intercept\newline(B) Slope and y y -intercept\newline(C) Slope and a point that is not an intercept\newline(D) x x -intercept and y y intercept\newline(E) y y -intercept and a point that is not an intercept\newline(F) Two points that are not intercepts

Full solution

Q. Hiro painted his room. After 33 hours of painting at a rate of 88 square meters per hour, he had 2828 square meters left to paint.\newlineLet y y represent the area (in square meters) left to paint after x x hours.\newlineWhich of the following information about the graph of the relationship is given?\newlineChoose 11 answer:\newline(A) Slope and x x -intercept\newline(B) Slope and y y -intercept\newline(C) Slope and a point that is not an intercept\newline(D) x x -intercept and y y intercept\newline(E) y y -intercept and a point that is not an intercept\newline(F) Two points that are not intercepts
  1. Calculate Initial Area: Determine the initial area left to paint before Hiro starts painting.\newlineHiro has painted for 33 hours at a rate of 88 square meters per hour. To find the initial area, we need to add the area he has painted to the area left to paint.\newlineCalculation: 33 hours ×\times 88 square meters/hour = 2424 square meters painted\newlineInitial area left to paint = 2424 square meters + 2828 square meters left = 5252 square meters
  2. Write Equation: Write the equation that represents the relationship between the area left to paint yy and the hours spent painting xx. Since Hiro paints at a constant rate, the slope mm of the line representing this relationship is the negative of the rate of painting because the area left to paint decreases as time increases. Slope mm = 8-8 (since the area decreases by 88 square meters per hour) The y-intercept bb is the initial area left to paint, which is 5252 square meters. Equation: y=8x+52y = -8x + 52
  3. Identify Given Information: Identify the given information based on the equation y=8x+52y = -8x + 52.\newlineThe slope of the line is given by the coefficient of xx, which is 8-8.\newlineThe y-intercept of the line is given by the constant term, which is 5252.\newlineTherefore, the information given is the slope and the y-intercept.

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