tell whether the lines for each pair of equations are parallel, perpendicular, or neither. y= -4x + 3 -2x + 8y = 5
To determine if two lines are parallel, perpendicular, or neither, we need to compare their slopes.
The given equations are:
1) y = -4x + 3
2) -2x + 8y = 5
To find the slope of the first equation (1), we can directly compare it to the slope-intercept form (y = mx + b) where m represents the slope. In this case, the slope of equation (1) is -4.
To find the slope of the second equation (2), we need to rewrite it in slope-intercept form.
Start by isolating y:
-2x + 8y = 5
8y = 2x + 5
Now divide by 8:
y = (2/8)x + 5/8
Simplify to get:
y = (1/4)x + 5/8
Comparing equation (2) to slope-intercept form, we can see that the slope of equation (2) is 1/4.
Now let's compare the slopes:
The slope of equation (1) is -4 and the slope of equation (2) is 1/4.
Since the slopes are not equal (they are not the same number or negatives of each other), the lines are neither parallel nor perpendicular.