Answer
$\color{blue}{y=x-7}$
Work Step by Step
RECALL:
(1) The slope-intercept form of a line's equation is:
$y=mx+b$
where $m$ = slope and $b$ = y-intercept
(2) Perpendicular lines have slopes whose product is $-1$.
The line we are looking for the equation of is perpendicular to the line $\\x+y=2$. Converting this equation into slope-intercept form gives:
$x+y=2
\\y=-x+2$
The slope of this line is $-1$.
This means that the slope of the line perpendicular to this line is $1$ (since $-1(1) = -1$).
Thus, the tentative equation of the line is:
$y=1(x) + b
\\y=x+b$
To find the value of $b$, substitute the x and y values of the point $(4, -3)$ into the tentative equation above to obtain:
$y=x+b
\\-3=4+b
\\-3-4=b
\\-7=b$
Thus, the equation of the line is $\color{blue}{y=x-7}$.
