Final answer:
The equation of the line perpendicular to 9x + 4y = -2 that contains the point (-2, -4) is y = (4/9)x - (4/9).
Step-by-step explanation:
To find the equation of a line that is perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The given line has the equation 9x + 4y = -2, which we can rewrite in slope-intercept form as y = (-9/4)x - (1/2). The slope of the given line is -9/4, so the slope of the line perpendicular to it would be the negative reciprocal, which is 4/9.
Now that we have the slope of the perpendicular line, we can use the point-slope form of a line to find its equation. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. We know that the point (-2, -4) lies on the line, so substituting these values into the point-slope form gives us y - (-4) = (4/9)(x - (-2)). Simplifying this equation gives us y + 4 = (4/9)(x + 2). Finally, we can rewrite this equation in slope-intercept form to get the final equation of the line: y = (4/9)x - (4/9).
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