Final answer:
The slope of the line with equation y = −2/3x is −2/3. This value reflects the rate of change in the 'y' value for each unit of change in the 'x' value. The slope is constant throughout the line.
Step-by-step explanation:
The slope of a linear equation in the form of y = mx + b is represented by the coefficient of x, which is m. In the case of the equation y = −2/3x, the slope is −2/3. This is because the line rises −2 units for every 3 units it moves to the right on the horizontal axis. It is important to note that the slope is the same all along a straight line, as illustrated by Figure A1 Slope and the Algebra of Straight Lines.
In the additional examples provided, where we are asked to find the slope between two points or when considering lines with the same slope as a line of best fit, the slope can be calculated by using the slope formula ((y2 - y1) / (x2 - x1)) for two points or by identifying the coefficient of x in the linear equation.