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What is an equation of the line that passes through (−9,12) and is perpendicular to the line y= 3/1​ x+6 whose equation is?

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Final answer:

The equation of the line that passes through (-9, 12) and is perpendicular to the line y = 3x + 6 is y = -\frac{1}{3}x + 9.

Step-by-step explanation:

The question asks to find the equation of a line that is perpendicular to the line given by y = \frac{3}{1}x + 6 and passes through the point (-9, 12). The slope of the given line is 3, which means that the slope of a line perpendicular to it will be the negative reciprocal, which is -\frac{1}{3}. Now, using the point-slope form y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes, we can substitute m = -\frac{1}{3}, x1 = -9, and y1 = 12 to get the equation of the perpendicular line.

Therefore, the equation of the perpendicular line is:
y - 12 = -\frac{1}{3}(x + 9).

To find the y-intercept, simplify the equation:
y - 12 = -\frac{1}{3}x - 3 -> y = -\frac{1}{3}x + 9.

The final equation of the line passing through (-9, 12) and perpendicular to y = 3x + 6 is y = -\frac{1}{3}x + 9.

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