16. Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y = -7/8x - 1
32x - 28y = -36
Show your work.
To determine if the lines 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 represents the slope. Comparing this equation to the given equation, we can see that the slope is -7/8.
To find the slope of the second equation, we can rewrite it in slope-intercept form.
32x - 28y = -36
-28y = -32x - 36
y = 32/28x + 36/28
y = 8/7x + 9/7
From this equation, we can see that the slope is 8/7.
Since the slopes of the two lines are different (-7/8 and 8/7), the lines are not parallel.
To determine if they are perpendicular, we can check if the product of their slopes is -1.
(-7/8)(8/7) = -7/7 = -1
The product of the slopes is -1, which means the lines are perpendicular.
In summary, the lines given by the pair of equations are perpendicular.