So the right options are:
![y=-\frac{2}{5}x-1](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B2%7D%7B5%7Dx-1)
![2x+5y = -5](https://tex.z-dn.net/?f=2x%2B5y%20%3D%20-5)
![y-1=-\frac{2}{5}(x+5)](https://tex.z-dn.net/?f=y-1%3D-%5Cfrac%7B2%7D%7B5%7D%28x%2B5%29)
Further explanation:
Given equation of line is:
2x+5y=10
We have to convert it into point-slope form
![2x+5y=10\\5y=-2x+10\\Dividing\ both\ sides\ by\ 5\\y=-\frac{2}{5}x+\frac{10}{5}\\y=-\frac{2}{5}x+2](https://tex.z-dn.net/?f=2x%2B5y%3D10%5C%5C5y%3D-2x%2B10%5C%5CDividing%5C%20both%5C%20sides%5C%20by%5C%205%5C%5Cy%3D-%5Cfrac%7B2%7D%7B5%7Dx%2B%5Cfrac%7B10%7D%7B5%7D%5C%5Cy%3D-%5Cfrac%7B2%7D%7B5%7Dx%2B2)
The co-efficient of x is the slope of the line
So,
![m= -\frac{2}{5}](https://tex.z-dn.net/?f=m%3D%20-%5Cfrac%7B2%7D%7B5%7D)
As the required line is parallel to given line, it will also have same slope.
Let m1 be the slope of required line
Then the line will be:
![y=m_1x+b](https://tex.z-dn.net/?f=y%3Dm_1x%2Bb)
Putting the value of slope
![y=\frac{2}{5}x+b](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2%7D%7B5%7Dx%2Bb)
Putting (-5,1) in the equation to find the value of b
![1=-\frac{2}{5}(-5)+b\\1=2+b\\b=1-2\\b=-1](https://tex.z-dn.net/?f=1%3D-%5Cfrac%7B2%7D%7B5%7D%28-5%29%2Bb%5C%5C1%3D2%2Bb%5C%5Cb%3D1-2%5C%5Cb%3D-1)
Putting the values of slope and b in equation
![y=-\frac{2}{5}x-1](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B2%7D%7B5%7Dx-1)
Multiplying the whole equation by 5 will give us:
5y = -2x-5
2x+5y = -5
Another form of equation of line is Point-slope form
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
Putting the values of slope and point in the equation, we get
![y-1=-\frac{2}{5}(x+5)](https://tex.z-dn.net/?f=y-1%3D-%5Cfrac%7B2%7D%7B5%7D%28x%2B5%29)
So the right options are:
![y=-\frac{2}{5}x-1](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B2%7D%7B5%7Dx-1)
![2x+5y = -5](https://tex.z-dn.net/?f=2x%2B5y%20%3D%20-5)
![y-1=-\frac{2}{5}(x+5)](https://tex.z-dn.net/?f=y-1%3D-%5Cfrac%7B2%7D%7B5%7D%28x%2B5%29)
Keywords: Point-Slope form, Parallel lines
Learn more about point slope form at:
#LearnwithBrainly