Question

Mathew reads equal numbers of pages of a book every week. The graph shows the number of pages of the book left to read, y, after x weeks: A graph titled Mathew’s Book Reading shows Number of Weeks on the x-axis and Number of Pages Left on the y-axis. The scale on the x-axis shows numbers from 0 to 6 at increments of 1, and the scale on the y-axis shows numbers from 0 to 210 at increments of 30. A straight line joins the ordered pairs 0, 150 and 1, 120 and 2, 90 and 3, 60 and 4, 30 and 5, 0. Which equation best models the relationship between x and y? y = −30x + 150 y = −5x + 30 y = −30x + 210 y = −5x + 150

Answer 1

The equation that best models the relationship between the number of weeks (x) and the number of pages left (y) in Mathew's book reading is y = -30x + 150, calculated using the slope formula and the points given.

Step-by-step explanation:

To determine which equation best models the relationship between the number of weeks (x) and the number of pages left (y) for Mathew's book reading, we need to find the equation of a line that fits the points given. This is a straight-line graph, and according to the description provided, the points (0, 150), (1, 120), (2, 90), (3, 60), (4, 30), and (5, 0) are on the line.

The general form of a straight-line equation is y = mx + b, where m is the slope and b is the y-intercept. Since the points lie on a straight line, and we know that for each week the number of pages left decreases by the same amount, we can calculate the slope by selecting any two points. Let's use the first two, (0, 150) and (1, 120). The slope (m) is the change in y divided by the change in x, so:

m = (y2 - y1) / (x2 - x1)
m = (120 - 150) / (1 - 0)
m = -30

The slope of -30 means that for each week that passes, Mathew reads 30 pages. To find the y-intercept (b), we can use the point where x = 0, which is the starting point of reading, and y = 150, the total number of pages Mathew started with. Therefore, b = 150. Plugging the slope and y-intercept into the general equation, we get y = -30x + 150.

This line decreases by 30 pages each week and starts at 150 pages, fitting all the points listed in the problem. Therefore, the equation that best models the relationship between weeks and pages left is y = -30x + 150.