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Two perpendicular lines intersect on the x-axis. If one line has the equation y = (2/3)x + 6, then what is the equation of the other line? Answer in general form.

A. 3x - 2y = 18
B. 2x + 3y = 18
C. 3x + 2y = 18
D. 2x - 3y = 18

1 Answer

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Final answer:

The equation of the perpendicular line is 3x + 2y = 0.

Step-by-step explanation:

To find the equation of the other line that is perpendicular to the given line, we need to determine its slope. Since the given line has a slope of 2/3, we know that the slope of the perpendicular line will be the negative reciprocal of 2/3. The negative reciprocal of 2/3 is -3/2. Therefore, the equation of the other line can be written in the form y = mx + b as y = (-3/2)x + b.

Now, we can use the fact that the lines intersect on the x-axis to find the y-intercept (b). Since the point of intersection is on the x-axis, the y-coordinate of the point is 0. Plugging in these values into the equation, we get 0 = (-3/2)(0) + b, simplifying to 0 = 0 + b. Therefore, b = 0. So, the equation of the other line is y = (-3/2)x.

User Roman Vottner
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