Final answer:
The slope of line HI in triangle HIJ can be determined if triangle DEF is known to be similar, with corresponding sides parallel; the slopes of corresponding sides in similar triangles are equal. In general, the slope of a straight line in algebra is defined as the ratio of the vertical change to the horizontal change between any two points on the line.
Step-by-step explanation:
In the scenario where triangle DEF is similar to triangle HIJ, the slope of line HI can be deduced using the concept of similar triangles and the properties of the coordinate plane.
Since the triangles are similar, corresponding sides are proportional and the angles between corresponding sides are equal. This implies that the angles that the lines creating the sides of the triangles make with the x-axis are also equal, which in turn means that the slopes of the corresponding sides are equal as well.
Therefore, to know the slope of line HI we would need the coordinates of points H and I. However, if we suppose that the triangle DEF has corresponding sides parallel to HIJ, with DE parallel to HI for example, then the slope of DE would equal the slope of HI.
In algebra, the slope of a straight line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. If the slope of a line in triangle DEF can be found or is given, and if that line corresponds to HI in triangle HIJ, then the slope of HI will be the same due to the concept of similar triangles in geometry.