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# equation of line

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Find the equation of a line passing through (15,-7) perpendicular to the line 5x+6y=11

Mar 10, 2021

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5x + 6y = 11

6y = -5x + 11

y = $$-\frac{5}{6} x + \frac{11}{6}$$

Since the slope is $$-\frac{5}{6}$$ , the perpendicular slope to it is $$\frac{6}{5}$$

y = mx + b  --> (15, -7)

$$-7 = \frac{6}{5}(15) + b$$

$$-7 = 18 + b$$

$$b = -25$$

This means the equation of this line is:
$$y = \frac{6}{5}x - 25$$

Mar 10, 2021