The slope of the line given by the equation $y = -2x + 7$ is $-2$.

In the equation $y = -2x + 7$, the slope is represented by the coefficient of $x$. This format is known as the slope-intercept form, expressed as

where $m$ denotes the slope and $c$ indicates the y-intercept. In this particular case, we have $m = -2$, which confirms that the slope is $-2$.

The slope of a line provides insight into its steepness and direction. A positive slope indicates that the line ascends as one moves from left to right, whereas a negative slope signifies a descent. Since the slope in this example is $-2$, the line descends as you move from left to right. Specifically, for every unit you move one unit to the right along the x-axis, the corresponding value of $y$ decreases by $2$ units.

Grasping the concept of slope is essential for graphing linear equations and analyzing the relationship between variables. In practical applications, the slope often represents rates of change, such as speed or cost per item. For instance, if you were to graph the cost of items with a slope of $-2$, it would imply that for each additional item purchased, the total cost decreases by $2$ units.