Final answer:
The equation of a line with a slope of 0 that passes through the point (-3, -8) is y = -8, representing a horizontal line.
Step-by-step explanation:
The student has asked for the equation of a line that passes through the point (-3, -8) with a slope of 0. The slope of a line indicates the steepness and direction the line moves. If a line has a slope of 0, it means that there is no rise along the vertical axis as the value of x changes, which indicates that the line is perfectly horizontal.
To write the equation of a line, we typically use the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept. Since the slope (m) is 0 in this case, the line will not rise or fall as x changes. This means that no matter what value x assumes, y will always be equal to -8, which is the y-coordinate of the point through which the line passes. Therefore, the equation of the line is y = -8.