standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
![(\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{4}}}\implies \cfrac{-3}{-2}\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-\stackrel{y_1}{1}=\stackrel{m}{\cfrac{3}{2}}(x-\stackrel{x_1}{4})](https://tex.z-dn.net/?f=%28%5Cstackrel%7Bx_1%7D%7B4%7D~%2C~%5Cstackrel%7By_1%7D%7B1%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B2%7D~%2C~%5Cstackrel%7By_2%7D%7B-2%7D%29%20~%5Chfill%20%5Cstackrel%7Bslope%7D%7Bm%7D%5Cimplies%20%5Ccfrac%7B%5Cstackrel%7Brise%7D%20%7B%5Cstackrel%7By_2%7D%7B-2%7D-%5Cstackrel%7By1%7D%7B1%7D%7D%7D%7B%5Cunderset%7Brun%7D%20%7B%5Cunderset%7Bx_2%7D%7B2%7D-%5Cunderset%7Bx_1%7D%7B4%7D%7D%7D%5Cimplies%20%5Ccfrac%7B-3%7D%7B-2%7D%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-%5Cstackrel%7By_1%7D%7B1%7D%3D%5Cstackrel%7Bm%7D%7B%5Ccfrac%7B3%7D%7B2%7D%7D%28x-%5Cstackrel%7Bx_1%7D%7B4%7D%29)
![\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2(y-1)=2\left( \cfrac{3}{2}(x-4) \right)}\implies 2y-2 = 3(x-4)\implies 2y-2=3x-12 \\\\\\ -3x+2y-2=-12\implies -3x+2y=-10\implies \stackrel{\times -1\textit{ to both sides}}{3x-2y=10}](https://tex.z-dn.net/?f=%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20%7D%5Cstackrel%7BLCD%7D%7B2%7D%7D%7B2%28y-1%29%3D2%5Cleft%28%20%5Ccfrac%7B3%7D%7B2%7D%28x-4%29%20%5Cright%29%7D%5Cimplies%202y-2%20%3D%203%28x-4%29%5Cimplies%202y-2%3D3x-12%20%5C%5C%5C%5C%5C%5C%20-3x%2B2y-2%3D-12%5Cimplies%20-3x%2B2y%3D-10%5Cimplies%20%5Cstackrel%7B%5Ctimes%20-1%5Ctextit%7B%20to%20both%20sides%7D%7D%7B3x-2y%3D10%7D)
We use the formula
where d is distance, s is speed and t is time.
![d = 64km*7.5](https://tex.z-dn.net/?f=d%20%3D%2064km%2A7.5)
![d = 480km](https://tex.z-dn.net/?f=d%20%3D%20480km)
Therefore, a car would tracel 480 km.
18-7n+1= -9
You just have to ignore the first thing it asks for, and then write out what it's saying. Since it's asking for the difference, you have to subtract what it tells you to. In this case they are asking for you to subtract 7 times a number from 18 which is the same as writing 18-7n. Then, go back to the first thing it asks for and that wants you to add one. You now have this: 18-7n+1. Now all you have to do is set it equal to whatever it asks you for, which is -9. The final product should look like this:
18-7n+1= -9
I hope this helps and if you could let me know if I helped, that would be greatly appreciated!
Angle B is also 54° because they are vertically opposite angles.
Now, you do 54+54=108 and then 360-108=252. (The angles should always add up to 360, so remember that) Because angles C and D are also vertically corresponding angles, they add up to 252, and each measure 126°
Hey there!
B in a slope intercept form equation is the the y intercept. It dictates where the line will cross the y axis, and therefore the line's placement altogether. This is because if there was no y intercept, the line would only be shaped by the slope, and would start at 0.
Hope this helped!