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------------------------------------------------ 2-4: MathXL for School: Practice and Problem Solving Copy 1

Write the equation of a line perpendicular to [tex]9x - 4y = -3[/tex] that passes through the point [tex](-9, 2)[/tex].

The equation of the line is [tex]y=[/tex]

(Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the expression.)

To find the equation of a line perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. Using this approach, we can easily solve the given problem and find the equation of the line passing through a given point.

Explanation:

To find the equation of a line perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The given line, 9x - 4y = -3, can be rewritten in slope-intercept form as y = (9/4)x + (3/4). The slope of this line is 9/4, so the slope of any line perpendicular to it is -4/9. Using the point-slope form of a linear equation, we can write the equation of the line passing through (-9,2) as y - 2 = (-4/9)(x + 9). Simplifying this equation gives us the final answer of y = (-4/9)x - (38/9).

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