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# Analytic geometry

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Find the equation of the line in slope intercept form that is perpendicular to 2x-3y-12=0 and passes through the point (-3, 5). show your work

Jul 7, 2021

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Rearrange the equation into slope-intercept form,

$$-3y = -2x+12 \\ y = \frac{2}{3}x -4$$

The line we are looking for is perpendicular meaning that it's slope is the negative and reciprocal of $\frac{2}{3}$,

$$y = -\frac{3}{2}x + b$$

We know it passes through (-3, 5) so we can plug that in,

$$5 = \frac{9}{2} + b \\ b = \frac{1}{2}$$

So our final equation for the line we are looking for is $$y = -\frac{3}{2}x + \frac{1}{2}$$

Jul 7, 2021