The equation of the line that passes through points (3 , -2) and (5 , -1)
is ![y+2=\frac{1}{2}(x-3)](https://tex.z-dn.net/?f=y%2B2%3D%5Cfrac%7B1%7D%7B2%7D%28x-3%29)
Step-by-step explanation:
The equation of a line in point slope form is:
, where m is the lope of the line and ![(x_{1},y_{1})](https://tex.z-dn.net/?f=%28x_%7B1%7D%2Cy_%7B1%7D%29)
are the coordinates of a point lies on the line
The slope of a line that contains points
and
is
![m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
Write the equation:
1. That passes through the points (3 , -2) and (5 , -1)
2. Put your answer in fully reduced point-slope form
Let point (3 , -2) =
and point (5 , -1) = ![(x_{2},y_{2})](https://tex.z-dn.net/?f=%28x_%7B2%7D%2Cy_%7B2%7D%29)
∵ ![m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
∴ ![m=\frac{-1-(-2)}{5-3}=\frac{-1+2}{2}=\frac{1}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-1-%28-2%29%7D%7B5-3%7D%3D%5Cfrac%7B-1%2B2%7D%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7D)
∵ The equation of the line is ![y-y_{1}=m(x-x_{1})](https://tex.z-dn.net/?f=y-y_%7B1%7D%3Dm%28x-x_%7B1%7D%29)
∵
= (3 , -2)
∵ m = ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
- Substitute the coordinates of the point and m in the equation
∴ ![y-(-2)=\frac{1}{2}(x-3)](https://tex.z-dn.net/?f=y-%28-2%29%3D%5Cfrac%7B1%7D%7B2%7D%28x-3%29)
∴ ![y+2=\frac{1}{2}(x-3)](https://tex.z-dn.net/?f=y%2B2%3D%5Cfrac%7B1%7D%7B2%7D%28x-3%29)
The equation of the line that passes through points (3 , -2) and (5 , -1)
is ![y+2=\frac{1}{2}(x-3)](https://tex.z-dn.net/?f=y%2B2%3D%5Cfrac%7B1%7D%7B2%7D%28x-3%29)
Learn more:
You can learn more about equation the line in brainly.com/question/12967961
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