line s passes through the points (2,7) and (6,1) line t passes through the point (5,2) and is perpendicular to line s what is th
e equation for line t
1 answer:
let's keep in mind that perpendicular lines have <u>negative reciprocal</u> slopes, hmmm what is the slope of line S anyway?
![\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-7}{6-2}\implies \cfrac{-6}{4}\implies -\cfrac{3}{2} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{3}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{2}{3}}\qquad \stackrel{negative~reciprocal}{\cfrac{2}{3}}}](https://tex.z-dn.net/?f=%5Cbf%20%28%5Cstackrel%7Bx_1%7D%7B2%7D~%2C~%5Cstackrel%7By_1%7D%7B7%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B6%7D~%2C~%5Cstackrel%7By_2%7D%7B1%7D%29%20%5C%5C%5C%5C%5C%5C%20slope%20%3D%20m%5Cimplies%20%5Ccfrac%7B%5Cstackrel%7Brise%7D%7B%20y_2-%20y_1%7D%7D%7B%5Cstackrel%7Brun%7D%7B%20x_2-%20x_1%7D%7D%5Cimplies%20%5Ccfrac%7B1-7%7D%7B6-2%7D%5Cimplies%20%5Ccfrac%7B-6%7D%7B4%7D%5Cimplies%20-%5Ccfrac%7B3%7D%7B2%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bperpendicular%20lines%20have%20%5Cunderline%7Bnegative%20reciprocal%7D%20slopes%7D%7D%20%7B%5Cstackrel%7Bslope%7D%7B-%5Ccfrac%7B3%7D%7B2%7D%7D%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cstackrel%7Breciprocal%7D%7B-%5Ccfrac%7B2%7D%7B3%7D%7D%5Cqquad%20%5Cstackrel%7Bnegative~reciprocal%7D%7B%5Ccfrac%7B2%7D%7B3%7D%7D%7D)
so, we're really looking for the equation of a line whose slope is 2/3 and runs through (5,2)

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3/4 = 6/8
2. 2/9 = 4/18
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3. 6/7 = 12/14
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4. 5/9 = 10/18
3/18 = 1/6
5. 1/6 = 2/12
1/9 = 2/18
6. 3/8 = 6/12
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