Final answer:
The slope of the equation x + y + 8 = 0 is -1, representing a decrease of 1 on the y-axis for every unit increase on the x-axis, and the y-intercept is -8.
Step-by-step explanation:
The student is asking how to determine the slope of a linear equation, specifically for the equation x + y + 8 = 0. To find the slope, this equation should first be rewritten in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Subtract x and 8 from both sides to isolate y:
y = -x - 8
Here, the slope (m) is -1, as the coefficient of x is -1. This indicates that there is a decrease of 1 on the vertical axis for every increase of 1 on the horizontal axis. Consequently, for the given equation the slope is -1 and the y-intercept (b) is -8, where the line crosses the y-axis at the point (0, -8).