Final answer:
The slope of the line that passes through the points (4,7) and (7,16) is calculated to be 3, representing the rise over the run between the two points.
Step-by-step explanation:
The slope of a line that passes through two points can be calculated using the formula for slope, which is the change in the y-values divided by the change in the x-values. The two points in question are (4,7) and (7,16). To find the slope, subtract the y-value of the second point from the y-value of the first point (16 - 7) and divide by the difference in x-values (7 - 4), resulting in a slope of 9/3 or 3.
The slope represents the steepness and direction of a line. An understanding of slope is foundational in algebra, as it illustrates how the m and b terms in the equation for a straight line determine the line's shape. In general, the slope is the same all along a straight line, making it a crucial characteristic of the line's identity within the Cartesian plane.