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]
