Correct me if I'm wrong please

1. Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y = –2x + 4
–5x + 10y = 5 (1 point)
A.parallel
B.perpendicular *
C.neither

2. Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y = -1/4x + 10
–2x + 8y = 6 (1 point)
A.parallel
B.perpendicular
C.neither *

So @Mia im correct??

1.B

2.C

You are correct in your answer for question 1, the lines for the pair of equations are perpendicular.

To determine whether two lines are parallel or perpendicular, we can examine their slopes. The slope of a line can be determined by comparing the coefficients of x and y in the equation when it is in slope-intercept form (y = mx + b). The slope, m, is the coefficient of x.

For the first pair of equations:
y = -2x + 4
-5x + 10y = 5

To determine the slope of the first equation (-2x + 4), we can compare it to the slope-intercept form. We see that the coefficient of x is -2, so the slope is -2.

To determine the slope of the second equation (-5x + 10y = 5), we can rearrange it into slope-intercept form by isolating y:
10y = 5x + 5
y = (5/10)x + 1/2
y = (1/2)x + 1/2

Comparing the coefficient of x in the second equation, we see that it is 1/2.

Since the slopes are negative reciprocals of each other (-2 and 1/2), the lines are perpendicular (option B).

For question 2, you are also correct. The lines for the pair of equations are neither parallel nor perpendicular.

Using the same method, the slope of the first equation (y = -1/4x + 10) is -1/4.

And the slope of the second equation (-2x + 8y = 6) can be rearranged into slope-intercept form:
8y = 2x + 6
y = (2/8)x + 3/4
y = (1/4)x + 3/4

Comparing the coefficient of x in the second equation, we see that it is 1/4.

Since the slopes are not negative reciprocals of each other (-1/4 and 1/4), the lines are neither parallel nor perpendicular (option C).