Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.

Question

1
y=-x =-x+10
-2x + 8y = 6
(1 point)
O parallel
perpendicular
neither

Answer 1

The equations for the lines are y = -x + 10 and -2x + 8y = 6.

To determine whether the lines are parallel, perpendicular, or neither, we can check the slopes of the lines.

For the equation y = -x + 10, the slope is -1. This equation is in the form y = mx + b, where m represents the slope.

For the equation -2x + 8y = 6, we can rearrange it in slope-intercept form. Subtracting -2x from both sides gives us 8y = 2x + 6. Dividing both sides by 8, we get y = (2/8)x + 6/8, simplified to y = (1/4)x + 3/4. The slope for this equation is 1/4.

Since the slopes of the two lines are different, they are not parallel.

To determine whether they are perpendicular or neither, we can check if the product of their slopes is -1. The product of -1 and 1/4 is -1/4, which is not equal to -1. Therefore, the lines are neither parallel nor perpendicular.