Tell whether the lines for each pair of equations are parallel perpendicular or neither.
Y= -2x + 4
-5+10y=5
I think perpendicular
Next question is same kind-
Y=-1/4x+10
-2x+8y=6
I think it's neither
To determine whether two lines are parallel, perpendicular, or neither, we need to compare their slopes.
For the first pair of equations:
1. Y = -2x + 4
2. -5 + 10y = 5
To compare the slopes, let's convert both equations into slope-intercept form (y = mx + b), where m represents the slope:
1. Y = -2x + 4 -> slope = -2
2. -5 + 10y = 5 -> 10y = 10, y = 1 -> slope = 0 (since it's a horizontal line)
Since the slopes are different (-2 and 0), the lines are neither parallel nor perpendicular.
For the second pair of equations:
1. Y = -1/4x + 10
2. -2x + 8y = 6
Again, let's convert both equations into slope-intercept form:
1. Y = -1/4x + 10 -> slope = -1/4
2. -2x + 8y = 6 -> 8y = 2x + 6, y = 1/4x + 3/4 -> slope = 1/4
Since the slopes are negative reciprocals (-1/4 and 1/4), the lines are perpendicular.
So, for the first pair of equations, the lines are neither parallel nor perpendicular.
And for the second pair of equations, the lines are perpendicular.
To determine whether the lines for a pair of equations are parallel, perpendicular, or neither, we need to examine their slopes.
For the first pair of equations:
Y = -2x + 4
-5 + 10y = 5
First, let's rewrite the second equation in slope-intercept form (y = mx + b):
10y = 10
y = 1
Comparing the equations' slopes, we find that the first equation has a slope of -2, and the second equation has a slope of 0 (since it is a horizontal line).
Since the slopes are different and one is zero, these lines are perpendicular.
For the second pair of equations:
Y = -1/4x + 10
-2x + 8y = 6
Let's rewrite the second equation in slope-intercept form (y = mx + b):
8y = 2x + 6
y = 1/4x + 3/4
Comparing the slopes, we find that the first equation has a slope of -1/4, and the second equation has a slope of 1/4.
Since the slopes are negative reciprocals of each other, these lines are perpendicular.
Therefore, your answers are correct:
First pair of equations: Perpendicular
Second pair of equations: Perpendicular
the first has a slope of -2, comparing it to y = mx+b
2nd:
I will assume you meant:
-5x + 10y = 5
10y = 5x + 5
y = (1/2)x + 1/2
so the slopes are 1/2 and -2,
well, now you can be 100% sure they are perpendicular
repeat for #2
remember , if the are parallel, the must have the same slope