What is the equation of the line that passes through (4, -1) and (-2, 3)?
1 answer:
Answer:
2x + 3y - 5 = 0
Step-by-step explanation:
(4 , -1) & (-2,3)
![Slope =\frac{y_{2}-y_{1}}{x_{2}-x_1}}\\\\=\frac{3-[-1]}{-2-4}\\\\=\frac{3+1}{-6}\\\\=\frac{4}{-6}\\\\=\frac{-2}{3}](https://tex.z-dn.net/?f=Slope%20%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_1%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B3-%5B-1%5D%7D%7B-2-4%7D%5C%5C%5C%5C%3D%5Cfrac%7B3%2B1%7D%7B-6%7D%5C%5C%5C%5C%3D%5Cfrac%7B4%7D%7B-6%7D%5C%5C%5C%5C%3D%5Cfrac%7B-2%7D%7B3%7D)
m = -2/3; (4 , -1)
y - y1 = m(x - x1)
![y - [-1]= \frac{-2}{3}(x-4)\\\\y + 1 =\frac{-2}{3}x -4*\frac{-2}{3}\\\\y + 1 =\frac{-2}{3}x+\frac{8}{3}](https://tex.z-dn.net/?f=y%20-%20%5B-1%5D%3D%20%5Cfrac%7B-2%7D%7B3%7D%28x-4%29%5C%5C%5C%5Cy%20%2B%201%20%3D%5Cfrac%7B-2%7D%7B3%7Dx%20-4%2A%5Cfrac%7B-2%7D%7B3%7D%5C%5C%5C%5Cy%20%2B%201%20%3D%5Cfrac%7B-2%7D%7B3%7Dx%2B%5Cfrac%7B8%7D%7B3%7D)
Multiply the equation by 3
3y + 3 = -2x + 8
3y = -2x + 8 - 3
3y = -2x + 5
2x + 3y - 5 = 0
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