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Find the equation of the line that passes through the point (3,-5) and is perpendicular to the line y=1/9x-2. Write the equation using the slope-intercept form.

User Jay Elrod
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Final answer:

To find the equation of a line that is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line. The equation of the perpendicular line is y = -9x + 22.

Step-by-step explanation:

To find the equation of a line that is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line.

The given line is y = 1/9x - 2, so the slope is 1/9.

The negative reciprocal of 1/9 is -9.

Now we have the slope of the perpendicular line. We can use the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Substituting the point (3, -5) and the slope -9 into the equation, we have y - (-5) = -9(x - 3).

Simplifying the equation gives us y + 5 = -9x + 27.

Finally, rearranging the equation into the slope-intercept form, we get y = -9x + 22.

User Asami
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