Tell whether the lines y=-4x+3 and -2x+8y=5 are parallel, perpendicular, or neither.
To determine whether the lines are parallel, perpendicular, or neither, we compare the slopes of the lines.
The first line, y = -4x + 3, is in slope-intercept form (y = mx + b) where the slope is the coefficient of x. Therefore, the slope of this line is -4.
The second line, -2x + 8y = 5, is not in slope-intercept form. Let's rearrange it to get it in that form: 8y = 2x + 5 => y = (2/8)x + 5/8. This is equivalent to y = (1/4)x + 5/8. Thus, the slope of this line is 1/4.
Since the slopes of the two lines are not equal and their product is not -1, they are neither parallel nor perpendicular.