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Conrad read a 180-page book cover to cover in a single session, at a constant rate. It took him 6 hours. Let y represent the number of pages left to read after t 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

Conrad read a 180180-page book cover to cover in a single session, at a constant rate. It took him 66 hours.\newlineLet \newlineyy represent the number of pages left to read after \newlinett hours.\newlineWhich of the following information about the graph of the relationship is given?\newlineChoose 11 answer:\newline(A) Slope and \newlinexx-intercept\newline(B) Slope and \newlineyy-intercept\newline(C) Slope and a point that is not an intercept\newline(D) \newlinexx-intercept and \newlineyy intercept\newline(E) \newlineyy-intercept and a point that is not an intercept\newline(F) Two points that are not intercepts

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Q. Conrad read a 180180-page book cover to cover in a single session, at a constant rate. It took him 66 hours.\newlineLet \newlineyy represent the number of pages left to read after \newlinett hours.\newlineWhich of the following information about the graph of the relationship is given?\newlineChoose 11 answer:\newline(A) Slope and \newlinexx-intercept\newline(B) Slope and \newlineyy-intercept\newline(C) Slope and a point that is not an intercept\newline(D) \newlinexx-intercept and \newlineyy intercept\newline(E) \newlineyy-intercept and a point that is not an intercept\newline(F) Two points that are not intercepts
  1. Determine reading rate: Determine the rate at which Conrad reads.\newlineConrad read a 180180-page book in 66 hours, so his reading rate is the number of pages divided by the number of hours.\newlineRate = Total pagesTotal time\frac{\text{Total pages}}{\text{Total time}}\newlineRate = 180 pages6 hours\frac{180 \text{ pages}}{6 \text{ hours}}\newlineRate = 3030 pages per hour
  2. Write equation for pages left: Write the equation for the number of pages left to read after t hours.\newlineSince Conrad reads at a constant rate, the number of pages he has left to read decreases linearly over time. The equation for the number of pages left, y, after t hours is:\newliney = \text{Total pages} - (\text{Rate} \times t)\newliney = 180180 - (3030 \times t)
  3. Identify y-intercept: Identify the y-intercept of the graph.\newlineThe y-intercept occurs when t=0t = 0, which is the starting point before Conrad begins reading. Plugging t=0t = 0 into the equation gives us the y-intercept.\newliney=180−(30×0)y = 180 - (30 \times 0)\newliney=180y = 180\newlineThe y-intercept is the point (0,180)(0, 180), which represents the total number of pages Conrad has to read before he starts reading.
  4. Identify slope: Identify the slope of the graph.\newlineThe slope of the graph is the rate at which the number of pages left to read is changing with respect to time. In the equation y=180−(30×t)y = 180 - (30 \times t), the coefficient of tt is −30-30, which is the slope.\newlineSlope = −30-30 pages per hour
  5. Determine x-intercept: Determine if there is an x-intercept and what it represents.\newlineThe x-intercept occurs when y=0y = 0, which means there are no pages left to read. To find the x-intercept, set yy to 00 and solve for tt.\newline0=180−(30×t)0 = 180 - (30 \times t)\newline30×t=18030 \times t = 180\newlinet=18030t = \frac{180}{30}\newlinet=6t = 6\newlineThe x-intercept is the point (6,0)(6, 0), which represents the time it took Conrad to finish reading the book.
  6. Choose correct answer: Choose the correct answer based on the information given.\newlineWe have identified both the slope of the graph (−30-30 pages per hour) and the y-intercept (0,180)(0, 180). Therefore, the correct answer is:\newline(B) Slope and y-intercept

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