17. Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
Show your work.
`y = -1/4x + 10`
`-2x + 8y = 6`
To determine whether the lines are parallel, perpendicular, or neither, we need to compare the slopes of the two lines.
The given equation, `y = -1/4x + 10`, is in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope is -1/4.
To compare the slopes, we need to rewrite the second equation, `-2x + 8y = 6`, in slope-intercept form. We can do this by isolating y:
`-2x + 8y = 6`
8y = 2x + 6
y = (2/8)x + 6/8
y = 1/4x + 3/4
Now we can see that the slope of the second equation is 1/4.
Since the slopes of the two lines are negative reciprocals of each other (-1/4 and 1/4), the lines are perpendicular.
Therefore, the answer is perpendicular.