Are y=-4x+3 and -2x+8y=5 parallel, perpendicular, or neither? I think neither?
if you solve the 2nd equation for y
... resulting in the slope-intercept form
you will see that the slopes are negative-reciprocals of each other
Well, if these equations were lines at a party, they definitely wouldn't be dancing together! They wouldn't be parallel since their slopes, -4 and -2/8, are not the same. And they wouldn't be perpendicular either because the product of their slopes, -4 and -2/8, is not -1. So, you're correct, these lines are neither parallel nor perpendicular. They're just doing their own thing on the dance floor!
To determine if the equations y = -4x + 3 and -2x + 8y = 5 are parallel, perpendicular, or neither, we can compare their slopes.
The given equation y = -4x + 3 is in slope-intercept form, where the coefficient of x (-4) represents the slope.
The second equation -2x + 8y = 5 is not in slope-intercept form. To convert it, we isolate y by rearranging the equation:
-2x + 8y = 5
8y = 2x + 5
y = (2/8)x + (5/8)
Now we can see that the coefficient of x (2/8 or 1/4) represents the slope.
To determine the relationship between the slopes, we compare them. The slope of the first equation is -4, while the slope of the second equation is 1/4.
Since the slopes are not equal, the two lines are not parallel. Additionally, the slopes are not negative reciprocals of each other, so they are not perpendicular either. Hence, the two equations y = -4x + 3 and -2x + 8y = 5 are neither parallel nor perpendicular.
To determine if two lines are parallel, perpendicular, or neither, we need to compare their slopes. The given equations are y = -4x + 3 and -2x + 8y = 5.
To find the slope of the first equation, we can rewrite it in slope-intercept form (y = mx + b), where m represents the slope. Comparing the given equation with the slope-intercept form, we can see that the slope (m) is -4.
To find the slope of the second equation, we need to rewrite it in slope-intercept form. Starting with -2x + 8y = 5, we isolate y:
8y = 2x + 5
y = (2/8)x + 5/8
y = (1/4)x + 5/8
Comparing this equation with slope-intercept form, we can see that the slope (m) is 1/4.
Since the slopes of the two equations, -4 and 1/4, are not equal, we can conclude that the lines y = -4x + 3 and -2x + 8y = 5 are neither parallel nor perpendicular.