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ANSWER

[tex]y - x = - 1[/tex]

EXPLANATION

The required equation passes through:

(4,3) and is perpendicular to x+y=4.

Rewrite the given equation in slope-intercept form:

[tex]y = - x + 4[/tex]

The slope of this line is -1.

The slope of the required line is perpendicular to this line, so we find the negative reciprocal of this slope.

[tex] m= - \frac{1}{ - 1} = 1[/tex]

The equation of the line can be found using:

[tex]y - y_1 = m(x - x_1)[/tex]

We substitute the slope and point to obtain:

[tex]y - 3 = 1(x - 4)[/tex]

We simplify to get:

[tex]y - 3 = x - 4[/tex]

[tex]y - x = - 4 + 3[/tex]

The required equation is

[tex]y - x = - 1[/tex]

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