The equation of line passing through the points (3,3) and (-3,5) is:
x+3y=12
Step-by-step explanation:
Given points are:
(x1, y1) = (3,3)
(x2, y2) = (-3, 5)
The general form of slope-intercept form is:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
We have to find slope first
![m=\frac{y_2-y_1}{x_2-x_1}\\=\frac{5-3}{-3-3}\\=\frac{2}{-6}\\=-\frac{1}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%3D%5Cfrac%7B5-3%7D%7B-3-3%7D%5C%5C%3D%5Cfrac%7B2%7D%7B-6%7D%5C%5C%3D-%5Cfrac%7B1%7D%7B3%7D)
Putting the value of m in general form
![y=-\frac{1}{3}x+b](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B3%7Dx%2Bb)
To find the value of b, putting (3,3) in equation
![3=-\frac{1}{3}(3)+b\\3=-1+b\\b=4](https://tex.z-dn.net/?f=3%3D-%5Cfrac%7B1%7D%7B3%7D%283%29%2Bb%5C%5C3%3D-1%2Bb%5C%5Cb%3D4)
Putting the values of m and b in general form
![y=-\frac{1}{3}x+4](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B3%7Dx%2B4)
Multiplying both sides by 3
![3y=-x+12\\x+3y=12](https://tex.z-dn.net/?f=3y%3D-x%2B12%5C%5Cx%2B3y%3D12)
The equation of line passing through the points (3,3) and (-3,5) is:
x+3y=12
Keywords: Equation of line, Standard form
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