Question

Is the line y = 3x – 7 parallel or perpendicular to 3x + 9y = 9? Explain your answer.

Answer 1

Okay, so we have y = 3x - 7 and it's put in the y = mx + b form so we can easily identify the slop which is 3 (the m).

Now for the other one it's gonna be a little tricky. We have to set it up into the y = mx + b form. So first I would subtract 3x from both sides to get
9y=-3x+ 9

And then divide 9 from both sides to get
y = -3/9 x + 9/9

Which can be simplified to
y = -1/3 x + 1

Now we can identify the slop for this is -1/3

So what can we do with knowing the slopes? Well if the slopes are the same then they are parallel which in this case they are not so then what are they? Notice that -1/3 is the reciprocal (the flip) of 3 (which can also be written like 3/1). Not only this but it's negative, the opposite sign. This means it is the opposite reciprocal which means it is perpendicular.

I hope this helps! Feel free to let me know if you have any questions!

- mathwizzard3

Answer 2

Sample Response: The lines are perpendicular because perpendicular lines have slopes that are opposite reciprocals. To compare the slopes, you can rewrite the second equation in slope-intercept form as y = (–1/3)x + 1. The slope of the given line is 3, and the slope of the second line is –1/3. These have a product of –1, which means they are opposite reciprocals. Thus, the two lines are perpendicular.