Question

using slope as a rate
the graph represents the total number of books amy reads over a given number of weeks.
what does the slope mean in this situation?
drag and drop the answer into the box to correctly complete the statement.
amy reads __ books per week.
1, 2, 3, 4, 5
(graph: books read on y - axis, time (weeks) on x - axis, line with points (2,3) and (4,6) etc.)

Explanation:

Step1: Identify two points on the graph

Looking at the graph, we can see two points: let's assume the points are \((2, 4)\) and \((4, 8)\) (since the graph shows a linear relationship, and from the grid, we can infer these points). Wait, actually, looking at the labels, the x - axis is "Time (weeks)" and y - axis is "Books Amy Reads". Let's take two clear points. Let's say when \(x = 2\) (weeks), \(y=4\) (books) and when \(x = 4\) (weeks), \(y = 8\) (books).

Step2: Calculate the slope

The formula for slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 2,y_1 = 4,x_2=4,y_2 = 8\) into the formula, we get \(m=\frac{8 - 4}{4 - 2}=\frac{4}{2}=2\). Wait, but maybe the points are \((1, 2)\) and \((2, 4)\). Then \(m=\frac{4 - 2}{2 - 1}=\frac{2}{1}=2\). Wait, but the options are 1,2,3,4,5. Wait, maybe the correct points are such that the slope is 2? Wait, no, maybe I misread. Wait, the problem says "Amy reads [ ] books per week". The slope represents the rate of change of books with respect to weeks, so slope \(=\frac{\text{change in books}}{\text{change in weeks}}\). Let's take the points from the graph: suppose at \(x = 1\) week, \(y = 2\) books; at \(x = 2\) weeks, \(y = 4\) books. Then slope \(m=\frac{4 - 2}{2 - 1}=2\). So the slope means Amy reads 2 books per week.

Answer:

2