Final answer:
The slope between the points (0, –5) and (–9,1) is -2/3, which is found using the slope formula. Positive slopes rise, negative slopes fall, and zero slopes are horizontal lines.
Step-by-step explanation:
To find the slope of a line passing through two points (0, –5) and (–9,1), we use the formula for the slope (m), which is m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
Substituting the given points into the formula, we get m = (1 - (-5)) / (-9 - 0), which simplifies to m = (1 + 5) / (-9), and further simplifies to m = 6 / (-9), resulting in a slope of m = -2/3.
Regarding slope and its characteristics on a graph, a positive slope means the line rises as it moves from left to right, a negative slope means the line falls as it moves from left to right, and a zero slope indicates a horizontal line.