California Assessment of Student Performance and Progress (CAASPP) Math Practice Exam

What is the slope of the line passing through the points (2, 3) and (4, 7)?

1. 1

2. 2

3. 3

4. 4

The correct answer is: 2

To determine the slope of the line passing through the points (2, 3) and (4, 7), we can use the formula for the slope, which is defined as the change in the y-coordinates divided by the change in the x-coordinates between the two points. The formula is: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Here, we can assign the coordinates: \( (x_1, y_1) = (2, 3) \) and \( (x_2, y_2) = (4, 7) \). Applying these values to the formula gives us: \[ \text{slope} = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2 \] Therefore, the slope of the line that passes through these two points is 2. This indicates that for every unit the line moves horizontally to the right (increasing x), the value of y increases by 2 units, illustrating a positive correlation between x and y. In the context of the other available choices, the reasoning shows that