Ontario Mathematics Proficiency Practice Test

To find the slope of the line that passes through the points (2, 3) and (4, 7), you can use the formula for slope, which is given by the change in the y-coordinates divided by the change in the x-coordinates.

The formula is:

\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

In this case, let (x₁, y₁) be (2, 3) and (x₂, y₂) be (4, 7). Plugging these values into the formula gives:

\[ \text{slope} = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2 \]

This means that for every 2 units the line rises (the change in y), it runs 1 unit (the change in x). A slope of 2 indicates a relatively steep line that rises quickly as it moves from left to right on the coordinate plane.

Understanding the slope is crucial because it describes the direction and steepness of the line. A positive slope indicates that as x increases, y also increases, which