Question

what is the equation of the line that passes through the point (-1, 6) and has a slope of -1?

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.
Here, $x_1=-1$, $y_1 = 6$ and $m=-1$.

Step2: Substitute values into point - slope form

Substitute $x_1=-1$, $y_1 = 6$ and $m =- 1$ into the point - slope formula:
$y-6=-1(x - (-1))$
Simplify the right - hand side: $y - 6=-1(x + 1)$

Step3: Expand and simplify to slope - intercept form

Expand the right - hand side: $y-6=-x - 1$
Add 6 to both sides of the equation: $y=-x - 1+6$
Simplify the constant terms: $y=-x + 5$
We can also write it in standard form $x+y=5$ (but slope - intercept form is also a valid equation of the line).

Answer:

The equation of the line is $y=-x + 5$ (or $x + y=5$)