Practice Describing, Finding, and Interpreting Slope

What term describes the slope of the line of a graph representing the data in the table?

The slope of a line graphed to represent the volume of water in a pool over time would be described as ______.

What is the general equation of a straight line?

The slope of a line graphed to represent the volume of water in a pool over time will be 6 and the equation of the line representing the table y = -6x + 50.

The general equation of a straight line is y = mx + c, where m is the slope of the line which represents the unit rate of change of y with respect to x, and c is the y-intercept - the point where the graph intersects the y-axis.

The equation of a straight line can also be written as Ax + By + C = 0, By = -Ax - C, or y = (-A/B)x - (C/A).

To find the slope of the line from the given table, we use the formula m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are two points on the line. Calculating the slope from the table, we get m = -6.

At x = 0, the y-coordinate is 50. Therefore, the equation of the line representing the table is y = -6x + 50. This means that for every increase of 1 in x, y decreases by 6.

Refer to the graph attached, the slope of a line graphed to represent the volume of water in a pool over time will be 6 and the equation of the line representing the table is y = -6x + 50.