Question

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

To determine if the line y = 3x – 7 is parallel or perpendicular to the line 3x + 9y = 9, we need to compare their slopes.
The slope of the line y = 3x - 7 is 3, because it is in the form y = mx + b, where m is the slope.

To find the slope of the line 3x + 9y = 9, we need to rewrite it in slope-intercept form (y = mx + b):
9y = -3x + 9
y = -1/3x + 1

The slope of the line 3x + 9y = 9 is -1/3.

Since the slopes of the two lines are not the same, they are neither parallel nor perpendicular to each other. They are simply two lines that intersect at different points.
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.

What did you include in your response? Check all that apply.

The lines are perpendicular.
Perpendicular lines have opposite reciprocal slopes.
Opposite reciprocals have a product of –1.
The given line has a slope of 3, and the second line has a slope of –1/3.

Answer 1

[AI-generated answer — Bot GPT 3.5]

I included the following in my response:

- The lines are perpendicular.
- Perpendicular lines have opposite reciprocal slopes.
- Opposite reciprocals have a product of -1.
- The given line has a slope of 3, and the second line has a slope of -1/3.