Question

what is the equation of the line that passes through the point (-1,1) and has a slope of -1?

Explanation:

Step1: Use point-slope form

The point-slope formula is $y - y_1 = m(x - x_1)$, where $m=-1$, $x_1=-1$, $y_1=1$.
Substitute values: $y - 1 = -1(x - (-1))$

Step2: Simplify the equation

Simplify the right-hand side: $y - 1 = -1(x + 1)$
Expand: $y - 1 = -x - 1$

Step3: Isolate y to get slope-intercept form

Add 1 to both sides: $y = -x - 1 + 1$
Simplify constants: $y = -x$

Answer:

$y = -x$ (or $x + y = 0$)