Tell whether the lines for each pair of equations are parallel, perpendicular, or neither. y = –1/4x + 10 –2x + 8y = 6
To determine whether the lines given by each pair of equations are parallel, perpendicular, or neither, we need to compare the slopes of the two lines.
The first equation is in slope-intercept form, y = mx + b, where m is the slope. Comparing it to the given equation, y = -1/4x + 10, we see that the slope is -1/4.
The second equation, -2x + 8y = 6, can be rearranged to slope-intercept form as well. Subtracting -2x from both sides and dividing by 8, we get y = 1/4x + 3/4. Comparing this equation to the first one, we see that the slope is 1/4.
Since the slopes of the two lines are negative reciprocals of each other (-1/4 * 1/4 = -1), we can conclude that the lines are perpendicular to each other.