A student was given the line y=2/3x-1 and the point (-7, 1/2) and asked to find an equation that went through the given point an
d was perpendicular to the given line. The students answer was y=3/2x+11. Explain what the student did incorrectly the give the correct answer
1 answer:
keeping in mind that perpendicular lines have <u>negative reciprocal</u> slopes, hmmm what's the slope of y=2/3x-1 anyway?
![\bf \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}~\hspace{7em}y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x-1 \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20slope-intercept~form%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y%3D%5Cunderset%7By-intercept%7D%7B%5Cstackrel%7Bslope%5Cqquad%20%7D%7B%5Cstackrel%7B%5Cdownarrow%20%7D%7Bm%7Dx%2B%5Cunderset%7B%5Cuparrow%20%7D%7Bb%7D%7D%7D%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D~%5Chspace%7B7em%7Dy%3D%5Cstackrel%7B%5Cstackrel%7Bm%7D%7B%5Cdownarrow%20%7D%7D%7B%5Ccfrac%7B2%7D%7B3%7D%7Dx-1%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)

so, notice, "one of his mistakes" is that he used 3/2 as the slope, not -3/2.
so, we're really looking for a line whose slope is -3/2 and runs through (-7, 1/2).
![\bf (\stackrel{x_1}{-7}~,~\stackrel{y_1}{\frac{1}{2}})~\hspace{10em} slope = m\implies -\cfrac{3}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\cfrac{1}{2}=-\cfrac{3}{2}[x-(-7)]\implies y-\cfrac{1}{2}=-\cfrac{3}{2}(x+7) \\\\\\ y-\cfrac{1}{2}=-\cfrac{3}{2}x-\cfrac{21}{2}\implies y=-\cfrac{3}{2}x-\cfrac{21}{2}+\cfrac{1}{2}\implies y=-\cfrac{3}{2}x-10](https://tex.z-dn.net/?f=%5Cbf%20%28%5Cstackrel%7Bx_1%7D%7B-7%7D~%2C~%5Cstackrel%7By_1%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D%29~%5Chspace%7B10em%7D%20slope%20%3D%20m%5Cimplies%20-%5Ccfrac%7B3%7D%7B2%7D%20%5C%5C%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20%5Ctextit%7Bpoint-slope%20form%7D%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y-y_1%3Dm%28x-x_1%29%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D%5Cimplies%20y-%5Ccfrac%7B1%7D%7B2%7D%3D-%5Ccfrac%7B3%7D%7B2%7D%5Bx-%28-7%29%5D%5Cimplies%20y-%5Ccfrac%7B1%7D%7B2%7D%3D-%5Ccfrac%7B3%7D%7B2%7D%28x%2B7%29%20%5C%5C%5C%5C%5C%5C%20y-%5Ccfrac%7B1%7D%7B2%7D%3D-%5Ccfrac%7B3%7D%7B2%7Dx-%5Ccfrac%7B21%7D%7B2%7D%5Cimplies%20y%3D-%5Ccfrac%7B3%7D%7B2%7Dx-%5Ccfrac%7B21%7D%7B2%7D%2B%5Ccfrac%7B1%7D%7B2%7D%5Cimplies%20y%3D-%5Ccfrac%7B3%7D%7B2%7Dx-10)
You might be interested in
8+(6)(3)^2
8+(6)(9)
8+(54)
8+54
62
I hope it helps
if it's correct, say Thanks and mark Brainliest
If it's wrong, just rate 4 stars. Don't report or delete:)
Answer:
the answer is A {126,168,189}
Answer:
Step-by-step explanation: 3 x 100 + 4 x 10 + 5 x 1 Standard form is the reverse ...
Answer:
.
14
Step-by-step explanation:
I would choose A
You can simply try every answer and see which one gives you 16a-24ab