Rearrange the equation into slope intercept form
7x+3y=18
3y=-7x+18
y=-7x/3+18/3 so the slope of the reference line is -7/3
To be perpendicular to this line the slope must be the negative reciprocal of this...mathematically m1*m2=-1. So the slope of our perpendicular line is:
-7m/3=-1
-7m=-3
m=3/7 so our line so far is:
y=3x/7+b, using point (6,8) we can solve for b, the y-intercept
8=3(6)/7+b
8=18/7+b
56/7-18/7=b
38/7=b so our line is:
y=3x/7+38/7 or if you prefer
y=(3x+38)/7
I'm not certain but I think it's <span>4 2/8. </span>
Answer:
B
Step-by-step explanation:
B because the y-intercept is (0,-1) and another point is (5,9). Using the slope formula, 10/5=2 so the right equation is B.
keeping in mind that perpendicular lines have negative reciprocal slopes, hmmmm what's the slope of the equation above anyway?
![\bf x+y=6\implies y = \stackrel{\stackrel{m}{\downarrow }}{-1}x+6\qquad \impliedby \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} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20x%2By%3D6%5Cimplies%20y%20%3D%20%5Cstackrel%7B%5Cstackrel%7Bm%7D%7B%5Cdownarrow%20%7D%7D%7B-1%7Dx%2B6%5Cqquad%20%5Cimpliedby%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%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
so we're really looking for the equation of a line whose slope is 1 and runs through (-5,-6).
![\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-6})~\hspace{10em} \stackrel{slope}{m}\implies 1 \\\\\\ \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-\stackrel{y_1}{(-6)}=\stackrel{m}{1}[x-\stackrel{x_1}{(-5)}] \\\\\\ y+6=1(x+5)\implies y+6=x+5\implies y=x-1](https://tex.z-dn.net/?f=%5Cbf%20%28%5Cstackrel%7Bx_1%7D%7B-5%7D~%2C~%5Cstackrel%7By_1%7D%7B-6%7D%29~%5Chspace%7B10em%7D%20%5Cstackrel%7Bslope%7D%7Bm%7D%5Cimplies%201%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-%5Cstackrel%7By_1%7D%7B%28-6%29%7D%3D%5Cstackrel%7Bm%7D%7B1%7D%5Bx-%5Cstackrel%7Bx_1%7D%7B%28-5%29%7D%5D%20%5C%5C%5C%5C%5C%5C%20y%2B6%3D1%28x%2B5%29%5Cimplies%20y%2B6%3Dx%2B5%5Cimplies%20y%3Dx-1)
Congruent means they are the same size
To prove the two triangles are congruent you would need to know the length of at least two of the sides. If two sides were not known you would need to know the length of one side and at least one of the unknown angles.
