What is the equation of the line that passes through (4, -1) and (-2, 3)?

Solution:

Given, (4, -1) and (-2, 3)

We have to find the equation of the line.

The equation of the line that passes through two points is given by

\(\frac{y-y_{1}}{y_{2}-y_{1}}=\frac{x-x_{1}}{x_{2}-x_{1}}\)

So, \(\frac{y-(-1))}{3-(-1)}=\frac{x-4}{-2-4}\\\frac{y+1}{4}=\frac{x-4}{-6}\\\)

On simplification,

-6(y + 1) = 4(x - 4)

-6y - 6 = 4x - 16

On rearranging,

4x + 6y + 6 - 16 = 0

4x + 6y - 10 = 0

Dividing by 2 on both sides,

2x + 3y - 5 = 0

Therefore, the equation of the line is 2x + 3y - 5 = 0.

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What is the equation of the line that passes through (4, -1) and (-2, 3)?

Summary:

The equation of the line that passes through (4, -1) and (-2, 3) is 2x +3y - 5 = 0.