Final answer:
To find the equation of a line passing through a given point and perpendicular to a given line, we determine the slope of the original line and then find the negative reciprocal. Using the point-slope form, we can write the equation.
Step-by-step explanation:
To find an equation of the line that passes through the point (6, -1) and is perpendicular to the line 3x + 2y = 4, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
The given line 3x + 2y = 4 can be rewritten in slope-intercept form as y = -3/2x + 2. Therefore, the slope of the given line is -3/2.
The negative reciprocal of -3/2 is 2/3. Using the point-slope form, we can write the equation of the line passing through (6, -1) with a slope of 2/3 as y - (-1) = 2/3(x - 6). Simplifying the equation, we get y = 2/3x - 13/3.
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