Tell whether the lines for each pair of equations are parallel, perpendicular, or neither and explain why.
y = –4x + 3
–2x + 8y = 5
To determine if two lines are parallel, perpendicular, or neither, we need to look at their slopes. The first equation is in slope-intercept form (y = mx + b), where m is the slope. In this case, the slope is -4.
The second equation can be rewritten in slope-intercept form by manipulating the equation:
-2x + 8y = 5
8y = 2x + 5
y = (2/8)x + 5/8
y = (1/4)x + 5/8
Comparing the slope of the second equation (1/4) to the slope of the first equation (-4), we can see that they are neither equal nor opposite reciprocals. Therefore, the lines are neither parallel nor perpendicular.