To show the equality of the slopes of AC and AN using a proportion, one would compare the ratios of the vertical and horizontal changes (rise over run) of the two hypotenuses within similar right triangles on the coordinate grid.
The question pertains to the concept of slope in coordinate geometry and involves the comparison of slopes of different lines to establish a proportion. Given that similar right triangles are being considered, the slopes of the hypotenuses can be compared by taking the ratio of the corresponding sides. The slope is calculated as the 'rise over run,' which means the change in the y-coordinate (vertical change) divided by the change in the x-coordinate (horizontal change) for a line on the coordinate grid.
The proportion that can show the equality of slopes AC and AN would depend on the specific coordinate of those points. However, generally, if we have two similar triangles, the proportion could be stated as (difference in y-coordinates of AC) / (difference in x-coordinates of AC) = (difference in y-coordinates of AN) / (difference in x-coordinates of AN), assuming that AC and AN are corresponding hypotenuses of the right triangles mentioned.