Final answer:
The slope of the line y = 7 - 2/3x is -2/3 and the y-intercept is 7. The slope represents a decrease of 2/3 on the y-axis per unit increase on the x-axis, and the line crosses the y-axis at the point (0, 7).
Step-by-step explanation:
To find the slope and y-intercept of the line given by the equation y = 7 - \(rac{2}{3}\)x, we will look at its terms. The equation is already in slope-intercept form, which is written as y = mx + b, where m is the slope and b is the y-intercept of the line.
The coefficient of x is the slope of the line, so in this case the slope m is -\(\frac{2}{3}\). This indicates that for every increase of 1 on the horizontal axis, there is a decrease of \(\frac{2}{3}\) on the vertical axis, since the slope is negative.
The constant term represents the y-intercept, which is the point where the line intersects the y-axis. Here, the y-intercept b is 7. This is the point (0, 7) on the graph, where the line crosses the y-axis.