Answer:
![\large\boxed{y-3=-\dfrac{1}{3}(x+6)-\text{point-slope form}}\\\boxed{y=-\dfrac{1}{3}x+1-\text{slope-intercept form}}\\\boxed{x+3y=3-\text{standard form}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7By-3%3D-%5Cdfrac%7B1%7D%7B3%7D%28x%2B6%29-%5Ctext%7Bpoint-slope%20form%7D%7D%5C%5C%5Cboxed%7By%3D-%5Cdfrac%7B1%7D%7B3%7Dx%2B1-%5Ctext%7Bslope-intercept%20form%7D%7D%5C%5C%5Cboxed%7Bx%2B3y%3D3-%5Ctext%7Bstandard%20form%7D%7D)
Step-by-step explanation:
The point-slope form of an equation of a line:
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
m - slope
We have
![m=-\dfrac{1}{3},\ (-6,\ 3)\to x_1=-6,\ y_1=3](https://tex.z-dn.net/?f=m%3D-%5Cdfrac%7B1%7D%7B3%7D%2C%5C%20%28-6%2C%5C%203%29%5Cto%20x_1%3D-6%2C%5C%20y_1%3D3)
Substitute:
![y-3=-\dfrac{1}{3}(x-(-6))\\\\y-3=-\dfrac{1}{3}(x+6)](https://tex.z-dn.net/?f=y-3%3D-%5Cdfrac%7B1%7D%7B3%7D%28x-%28-6%29%29%5C%5C%5C%5Cy-3%3D-%5Cdfrac%7B1%7D%7B3%7D%28x%2B6%29)
Convert to the slope-intercept form
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
<em>use the distributive property</em>
<em>add 3 to both sides</em>
![y=-\dfrac{1}{3}x+1](https://tex.z-dn.net/?f=y%3D-%5Cdfrac%7B1%7D%7B3%7Dx%2B1)
Convert to the standard form
![Ax+By=C](https://tex.z-dn.net/?f=Ax%2BBy%3DC)
<em>multiply both sides by 3</em>
<em>add x to both sides</em>
![x+3y=3](https://tex.z-dn.net/?f=x%2B3y%3D3)
The answer is in the enclosed diagram
Answer: No, your friend is not correct. You cannot use a similarity transformation to turn a square into a rectangle. Here's why:
1) If you used a similarity transformation, the size and position of the shape would change, but the shape itself remains the same.
2) Squares and rectangles are NOT similar.* Referring to the first point I listed, if the shapes are not similar, then a similarity transformation cannot be used to turn one shape into another.
<em>*Similar means that the edges are proportional to one another, such as a square with sides of 4 meters vs a square with sides of 2 meters: the sides are different lengths, but the shape is the same.</em>
I hope this helps! Please feel free to comment below if you need any clarification. Have a good day, and good luck on your assignment. :)