Question

Which points are on the line passing through (2, 0) and (0, 1)?

a) (-1, 2), (4, -1), (-2, 3)
b) (-2, 0), (0, 2), (3, -1)
c) (1, 2), (-1, 3), (4, -2)
d) (3, -1), (-1, 2), (2, -1)

Answer 1

(4, -1) is on the line y = -0.5x + 1.

Answer 2

The equation of the line passing through (2, 0) and (0, 1) is y = -1/2x + 1. The point (3, -1) is on this line.

Step-by-step explanation:

To find which points are on the line passing through (2, 0) and (0, 1), we need to find the equation of the line first. The equation of a line can be determined using the slope-intercept form: y = mx + b, where m represents the slope of the line and b represents the y-intercept. To find the slope, we use the formula: m = (y2 - y1) / (x2 - x1). Using the points (2, 0) and (0, 1), we have m = (1 - 0) / (0 - 2) = -1/2.
The equation of the line passing through (2, 0) and (0, 1) can be written as y = -1/2x + b. To find b, we substitute one of the points into the equation. Using (2, 0), we have 0 = -1/2(2) + b. Simplifying this equation, we find b = 1.

Therefore, the equation of the line passing through (2, 0) and (0, 1) is y = -1/2x + 1. To determine which points are on this line, we substitute the x and y coordinates of each given point into the equation and check if the equation holds true.

Option d) (3, -1) is on the line, so the correct answer is d) (3, -1).