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

Solution:

Given: Equation is y = 3x - 7

The equation of the line in the slope-intercept form is y = mx+ c.

Comparing this with the given equation, we find that the slope of this line = 3 and y-intercept = -7

If lines are parallel, then their slopes will be equal. If lines are perpendicular, then the product of their slope will be -1

3x + 9y = 9

This can be rewritten in the slope-intercept form as

9y = -3x + 9

Divide the equation by 9

y = -1/3x + 1

Slope = -1/3

y intercept = 1

The slopes 3 and -1/3 are the negative reciprocals of each other. 3 × -1/3 = -1

Hence, the lines are perpendicular to each other.

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

Summary:

The line y = 3x - 7 is perpendicular to 3x + 9y = 9.