College Math Placement Practice Test

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Calculate the slope of the line defined by the points (1, 2) and (3, 8).

The correct answer is: 3

To find the slope of the line defined by the points (1, 2) and (3, 8), you use the formula for the slope, which is given by the change in y divided by the change in x, or: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] In this case, the coordinates of the points can be assigned as follows: - Point 1: (1, 2) with $x_1 = 1$ and $y_1 = 2$ - Point 2: (3, 8) with $x_2 = 3$ and $y_2 = 8$ Now plug the values into the slope formula: \[ m = \frac{8 - 2}{3 - 1} = \frac{6}{2} = 3 \] Thus, the slope of the line that passes through the points (1, 2) and (3, 8) is 3. This indicates that for every increase of 1 unit in the x-direction, the y-value increases by 3 units, reflecting a positively inclined line on