College Math Placement Practice Test

What is the equation of the line that passes through the points (2, −4) and (6, 10)?

1. y = −7/2x + 11/2

2. y = 7/2x + 11

3. y = −7x − 11/2

4. y = 7/2x − 11

The correct answer is: y = 7/2x − 11

To determine the equation of the line that passes through the two given points, (2, −4) and (6, 10), we first calculate the slope (m) of the line. The slope is determined by the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the coordinates of the points: - Point 1 (x₁, y₁) = (2, −4) - Point 2 (x₂, y₂) = (6, 10) Plugging in these values: \[ m = \frac{10 - (-4)}{6 - 2} = \frac{10 + 4}{6 - 2} = \frac{14}{4} = \frac{7}{2} \] With the slope calculated, we can now use the point-slope form of the equation of a line, which is: \[ y - y_1 = m(x - x_1) \] We can use either of our points. Choosing (2, -4): \[ y - (-4) = \frac{7}{2}(x - 2) \] \[ y