Question

this graph shows how the number of pages brad still has to write for a research paper depends on the number of hours he spends writing. total pages brad has to write. after 2 hours of writing, how many pages will brad have left to write? 4 pages, 3 pages, 1 page, 2 pages

Explanation:

Step1: Locate x=2 on the graph

Find the point where the number of hours (x - axis) is 2.

Step2: Find the corresponding y - value

At x = 2 (2 hours of writing), look at the y - axis (number of pages left) for the graph's point. The line passes through (2, 1)? Wait, no, wait. Wait, the initial point is (0,5), and the line goes to (3,0). Let's calculate the slope. Slope $m=\frac{0 - 5}{3 - 0}=-\frac{5}{3}$. The equation is $y-5=-\frac{5}{3}(x - 0)$, so $y = 5-\frac{5}{3}x$. When x = 2, $y=5-\frac{10}{3}=\frac{15 - 10}{3}=\frac{5}{3}\approx1.666$? Wait, no, maybe I misread the graph. Wait, looking at the graph, when x=1, y=? Let's check the grid. The y - axis is pages left, x - axis is hours. At x=0, y=5. At x=3, y=0. So between x=0 and x=3, the line goes from (0,5) to (3,0). So the equation is linear. Let's find the value at x=2. The change in x from 0 to 3 is 3, change in y is - 5. So per hour, the number of pages written is $\frac{5}{3}$ pages per hour. So in 2 hours, pages written is $2\times\frac{5}{3}=\frac{10}{3}$, pages left is $5-\frac{10}{3}=\frac{5}{3}\approx1.666$, but the options are 4,3,1,2. Wait, maybe I misread the graph. Wait, the graph: when x=1, y=? Let's look at the grid. The y - axis has 5 at x=0, then at x=1, the line is at y=? Wait, the first grid line after 0 on x is 1, y=? Wait, the graph is a straight line from (0,5) to (3,0). So when x=2, let's see the vertical line at x=2. The horizontal line from that point to y - axis. Wait, maybe the graph is drawn with x=0 (5), x=1 (3), x=2 (1), x=3 (0)? Wait, no, that would be slope - 2. Wait, 5 - 2x. At x=0, 5; x=1, 3; x=2, 1; x=3, - 1? No, that can't be. Wait, the options include 1 page. Wait, maybe the graph is as follows: the line goes from (0,5) to (3,0). So when x=2, the y - value is 5 - (5/3)*2≈1.666, but the options have 1 page. Wait, maybe the graph is actually with a slope of - 2. Let's check: if at x=0, y=5; x=1, y=3 (5 - 2); x=2, y=1 (5 - 4); x=3, y=-1 (no, that's wrong). But the graph ends at (3,0), so maybe the correct reading is that at x=2, the number of pages left is 1? Wait, no, the options are 4,3,1,2. Wait, maybe I made a mistake. Wait, let's re - examine the graph. The y - axis is "Number of pages left to write", x - axis "Hours spent writing". The line starts at (0,5) and goes down to (3,0). So when x=2, we can see the point. Let's count the grid squares. From x=0 to x=3, that's 3 units on x, 5 units on y. So each x unit (hour) corresponds to 5/3 y units (pages). But the options are integers. Wait, maybe the graph is drawn with x=0 (5), x=1 (4), x=2 (3), x=3 (2)? No, that would be slope - 1. Then at x=2, y=3. Wait, that's one of the options (3 pages). Wait, maybe I misread the initial point. Wait, the graph: the first point is (0,5), then at x=1, it's at y=4? No, the line is steep. Wait, maybe the correct way is to look at the graph's coordinates. Let's assume the graph is a straight line. Let's take two points: (0,5) and (3,0). The equation is $y = 5-\frac{5}{3}x$. When x=2, $y=5-\frac{10}{3}=\frac{5}{3}\approx1.666$, but the closest option is 1 page? No, 1 page is an option. Wait, maybe the graph is actually with points (0,5), (1,3), (2,1), (3,0). So at x=2, y=1. But the options have 1 page. Wait, but let's check the options again. The options are 4 pages, 3 pages, 1 page, 2 pages. Wait, maybe the correct answer is 1 page? Wait, no, maybe I made a mistake. Wait, let's think again. If the total pages he has to write is 5 (at x=0), and he writes for 2 hours, how many are left? Let's see the rate. From 0 to 3 hours, he finishes 5 pages. So rate is 5/3 pages per hour. In 2 hours, he writes 10/3≈3.333 pages, so pages left is 5 - 10/3≈1.666, which is close to 1 page. So the answer should be 1 page? Wait, no, the options: 4,3,1,2. Wait, maybe the graph is different. Wait, maybe the line is from (0,5) to (3,0), and when x=2, the y - value is 1. So the correct option is 1 page.

Answer:

1 page