Write a slope-intercept equation for a line passing through the point (3, - 2) t

Question

Write a slope-intercept equation for a line passing through the point (3, - 2) that is parallel to the line 3x + 4y = 7. Then write a second equation for a line passing through the point (3, - 2) that is perpendicular to the line 3x + 4y = 7. The equation of the parallel line is (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the expression.) The equation of the perpendicular line is (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the expression.)

Explanation / Answer

The given line is

3x + 4y = 7

Or, 4y = -3x + 7

Or, y = (-3/4)x + 7/4

So the slope of the line = -3/4

A) The slope of the parallel line passing through the point (3,-2) = -3/4

Now the equation of the parallel line passing through the point (3,-2) is

y - (-2) = -3/4(x - 3)

Or, y + 2 = (-3/4)x + 9/4

Or, y = (-3/4)x + 9/4 - 2

Or, y = (-3/4)x + 1/4

B) The slope of the perpendicular line passing through the point (3,-2) = 4/3

So the equation of the perpendicular line passing through the point (3,-2) is

y - (-2) = 4/3(x - 3)

Or, y + 2 = (4/3)x - 4

Or, y = (4/3)x - 6

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