Question

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

Answer 1

It is perpendicular. Because 3x + 9y = 9 in slope-intercept form would be -1/3x + 1, -1/3x would be the opposite of 3x. Therefore, it is perpendicular.

But if you want the sample response instead, here you go

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.

Answer 2

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.

Explanation:

I don't need to explain.