College Math Placement Practice Test

Which point lies on the line passing through (4, 5) with a slope of -2?

1. (4, 1)

2. (6, 2)

3. (5, 3)

4. (5, 7)

The correct answer is: (5, 3)

To determine which point lies on the line passing through the point (4, 5) with a slope of -2, we can use the point-slope form of a linear equation. The equation can be written as follows: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope. Substituting in our values: y - 5 = -2(x - 4). Now, we simplify this equation to find the line's equation: y - 5 = -2x + 8, y = -2x + 13. This is the equation of the line. Next, we can test each of the points given in the options to see if they satisfy this equation. For the point (5, 3): Substituting x = 5 into the equation: y = -2(5) + 13, y = -10 + 13, y = 3. Since the calculated y-value matches the y-coordinate of the point (5, 3), this point lies on the line. To verify the other points: - For (4, 1): Plugging in x