Question
A line passes through the point (4, 3) and is
perpendicular to the line 3x + 4y = 12. Find the equation of the new line.Solution
The slope of the line 3x + 4y = 12 is given by rearranging it into slope-intercept form: 3x + 4y = 12 4y = -3x + 12 y = -3/4 * x + 3. Thus, the slope of the given line is -3/4. The slope of the perpendicular line will be the negative reciprocal, i.e., 4/3. Now, using the point-slope form of the equation of a line: y - y1 = m(x - x1), Substitute the point (4, 3) and slope 4/3: y - 3 = 4/3(x - 4), Multiply both sides by 3 to eliminate the fraction: 3(y - 3) = 4(x - 4), 3y - 9 = 4x - 16, 3y = 4x - 7, Thus, the equation of the line is: 4x - 3y = 7. Answer: c)
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