Answer:
The equation of a line can be expressed in slope-intercept form as y = mx + b, where m is the slope of the line and b is the y-intercept.
We know that the slope of the line is -1, and that the line passes through the point (4, -6).
Substituting these values into the slope-intercept form of the equation, we get:
-6 = (-1)(4) + b
Simplifying this equation, we get:
-6 = -4 + b
Adding 4 to both sides, we get:
-2 = b
So the y-intercept of the line is -2, and the equation of the line in slope-intercept form is:
y = -x - 2
Alternatively, we could use the point-slope form of the equation of a line, which states that the equation of a line passing through the point (x1, y1) with slope m is given by:
y - y1 = m(x - x1)
Substituting the values of the point and slope, we get:
y - (-6) = -1(x - 4)
Simplifying this equation, we get:
y + 6 = -x + 4
Subtracting 6 from both sides, we get:
y = -x - 2
So we get the same equation as before.