Answer:
In slope-intercept form:
![\displaystyle y=\frac{2}{3}x+1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D%5Cfrac%7B2%7D%7B3%7Dx%2B1)
Or, in standard form:
![2x-3y=-3](https://tex.z-dn.net/?f=2x-3y%3D-3)
Step-by-step explanation:
We want to find the equation of the line that passes through the point (6, 5) and is perpendicular to the line whose equation is:
![2y+3x=6](https://tex.z-dn.net/?f=2y%2B3x%3D6)
Since the new line is perpendicular, its slope and the slope of the first equation will be negative reciprocals of each other.
So, find the slope of the first equation. Subtract 3<em>x</em> from both sides:
![2y=-3x+6](https://tex.z-dn.net/?f=2y%3D-3x%2B6)
And divide both sides by two:
![\displaystyle y=-\frac{3}{2}x+3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D-%5Cfrac%7B3%7D%7B2%7Dx%2B3)
So, the slope of the first equation is -3/2.
The slope of the new line is its negative reciprocal. So, the slope of the perpendicular line is 2/3.
Next, we also know that it passes through the piont (6, 5). We can use the point-slope form:
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
Where <em>m</em> is the slope and (<em>x₁, y₁</em>) is a point.
Substitute:
![\displaystyle y-(5)=\frac{2}{3}\left(x-6\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y-%285%29%3D%5Cfrac%7B2%7D%7B3%7D%5Cleft%28x-6%5Cright%29)
And we have our equation!
If desired, we can simplify it into slope-intercept form:
![\displaystyle \begin{aligned} y-5&=\frac{2}{3}x-4\\\\y&=\frac{2}{3}x+1\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20y-5%26%3D%5Cfrac%7B2%7D%7B3%7Dx-4%5C%5C%5C%5Cy%26%3D%5Cfrac%7B2%7D%7B3%7Dx%2B1%5Cend%7Baligned%7D)
Or, into standard form:
![\displaystyle \begin{aligned} y&=\frac{2}{3}x+1\\\\3y&=2x+3\\\\ 2x-3y&=-3\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20y%26%3D%5Cfrac%7B2%7D%7B3%7Dx%2B1%5C%5C%5C%5C3y%26%3D2x%2B3%5C%5C%5C%5C%202x-3y%26%3D-3%5Cend%7Baligned%7D)
Answer:
20 degreese i belive but hey if you would can we ft instead of you marking me brainlyist
Step-by-step explanation:
Answer:
C) 324 cm^3
Step-by-step explanation:
So you know the volume and 2 side lengths. 360 divided by 12 divided by 5 to find the third side. The third side is 360 / 60 (answer of 12x5), which is 6. Surface area of prism is 324 (c)
Answer:
There can be 9 arrays.
Step-by-step explanation:
We are asked that the number of arrays that Courtney can make with 36 photos.
The dimensions of the possible arrays are
Here, the array with 1 row by 36 columns and 36 rows by 1 column are different. (Answer)
Answer: 761 yd
split the figure into different pieces to make it easier
(23 x 7) + (40 x 15)
161 + 600
761
hope this helped :)