Question

Select whether the pair of lines is parallel, perpendicular, or neither. Γ = 2x + 4 and y = 28 - 10 a) Parallel

b) Perpendicular
c) Neither parallel nor perpendicular
d) Insufficient information to determine

Answer 1

The given lines, represented by the equations y = 2x + 4 and y = 28 - 10x, have slopes of 2 and -10 respectively. Since their slopes neither are equal nor negative reciprocals of each other, the lines are neither parallel nor perpendicular.

Step-by-step explanation:

To determine whether the pair of lines is parallel, perpendicular, or neither, we need to look at the slopes of the lines. The equation of a straight line is generally expressed as y = mx + b where m represents the slope and b represents the y-intercept. For the given equations y = 2x + 4 and y = 28 - 10x, the slopes are 2 and -10, respectively.

Lines are parallel if they have the same slope, and they are perpendicular if the product of their slopes is -1 (since perpendicular slopes are negative reciprocals of each other). However, in this case, since the slopes are 2 and -10, and 2 * (-10) = -20 ≠ -1, the lines are neither parallel nor perpendicular.

Therefore, the correct answer is: c) Neither parallel nor perpendicular.