College Math Placement Practice Test

What is the equation of the line that passes through the points (−2, 4) and (−4, −2)?

1. y = 3x + 10

2. y = −1/3x − 10

3. y = 3x − 10

4. y = 1/3x + 10

The correct answer is: y = 3x + 10

To find the equation of the line that passes through two points, specifically (−2, 4) and (−4, −2), we start by calculating the slope of the line using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting in the given points, we have: \[ m = \frac{-2 - 4}{-4 - (-2)} = \frac{-6}{-4 + 2} = \frac{-6}{-2} = 3 \] Now that we have the slope (m = 3), we can use the point-slope form of the equation of a line, which is: \[ y - y_1 = m(x - x_1) \] We can choose either point; using (−2, 4): \[ y - 4 = 3(x + 2) \] Distributing the slope: \[ y - 4 = 3x + 6 \] Now, solve for y: \[ y = 3x + 10 \] This matches the equation provided in option A. Therefore