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.
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.
1 answer