Line ℓ contains the points A(2,2) and B(3,6). Line k contains the points C(0,5) and D(1,9).
Yes, lines ℓ and k are parallel because the lines pass through the same points.
No, lines ℓ and k are not parallel because the slopes are not equal.
Yes, lines ℓ and k are parallel because the slopes are equal.
No, lines ℓ and k are not parallel because the lines do not pass through the same points.
Its the 3rd answer . The slopes are equal
No, lines ℓ and k are not parallel because the slopes are not equal.
The correct answer is:
No, lines ℓ and k are not parallel because the slopes are not equal.
To determine if two lines are parallel, we need to compare their slopes. The slope of a line can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
For line ℓ, the coordinates A(2,2) and B(3,6) can be used to find the slope:
slope_ℓ = (6 - 2) / (3 - 2) = 4 / 1 = 4
For line k, the coordinates C(0,5) and D(1,9) can be used to find the slope:
slope_k = (9 - 5) / (1 - 0) = 4 / 1 = 4
Since the slopes of lines ℓ and k are equal (both slopes are 4), we can conclude that the lines ℓ and k are parallel.