If a point (x, y) in a plane is equidistant from the points (-1,1) and (4,3), then:

A point (x, y) is equidistant from (-1, 1) and (4, 3) when the distances are equal.

Using the distance formula:

$\sqrt{(x - (-1))^2 + (y - 1)^2} = \sqrt{(x - 4)^2 + (y - 3)^2}$

$\sqrt{(x + 1)^2 + (y - 1)^2} = \sqrt{(x - 4)^2 + (y - 3)^2}$

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Squaring both sides:

$(x + 1)^2 + (y - 1)^2 = (x - 4)^2 + (y - 3)^2$

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Expanding the left side:

$(x + 1)^2 = x^2 + 2x + 1$

$(y - 1)^2 = y^2 - 2y + 1$

$x^2 + 2x + 1 + y^2 - 2y + 1 = x^2 + 2x + y^2 - 2y + 2$

Expanding the right side:

$(x - 4)^2 = x^2 - 8x + 16$

$(y - 3)^2 = y^2 - 6y + 9$

$x^2 - 8x + 16 + y^2 - 6y + 9 = x^2 - 8x + y^2 - 6y + 25$

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The equation becomes:

$x^2 + 2x + y^2 - 2y + 2 = x^2 - 8x + y^2 - 6y + 25$

Canceling $x^2$ and $y^2$ from both sides:

$2x - 2y + 2 = -8x - 6y + 25$

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Collecting like terms:

$2x + 8x - 2y + 6y = 25 - 2$

$10x + 4y = 23$

Therefore, the equation is $10x + 4y = 23$.