Which of the following pairs of lines are perpendicular? How do you know?

Hi mate:
Here is your explanation

Which of the following is perpendicular to 32=16y+64x

Possible Answers:
y=−x/4+7

y=4x+7

y=−4x+7

y=x+1/4

y=x/4+7

Correct
y=x/4+7

Explanation:
Two lines are perpendicular if and only if their slopes are negative reciprocals. To find the slope, we must put the equation into slope-intercept form, y=mx+b, where m equals the slope of the line. We begin by subtracting 16y from each side, giving us 32−16y=64x. Next, we subtract 32 from each side, giving us −16y=64x−32. Finally, we divide each side by −16, giving us y=−4x+2. We can now see that the slope is −4. Therefore, any line perpendicular to 32=16y+64x must have a slope of 1/4. Of the equations above, only y=x/4+7 has a slope of 1/4.

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