Question

complete the parts below
a) find the rise, run, and slope given by triangle abc.
rise
run
slope:
b) find the rise, run, and slope given by triangle def

Explanation:

Step1: Analyze Triangle ABC (Rise, Run, Slope)

To find the rise, we look at the vertical change between points B and A. Let's assume the coordinates: From the graph, B is at (2, 0) and A is at (3, 6) (estimating from the grid). The vertical change (rise) is \( 6 - 0 = 6 \). The horizontal change (run) is \( 3 - 2 = 1 \)? Wait, no, maybe better to check the right triangle. Wait, the right angle is at C, so B to C is run, C to A is rise? Wait, maybe the grid: Let's see, E and F are horizontal, so for ABC, the vertical leg (rise) and horizontal leg (run). Let's count the units. Suppose from B to C is 1 unit (run), and from C to A is 6 units (rise)? Wait, maybe the graph has B at (2,0), C at (3,0) (run 1), and A at (3,6) (rise 6). So rise = 6, run = 1, slope = rise/run = 6/1 = 6. Wait, maybe I misread. Wait, the problem is about triangle ABC: let's assume the coordinates. Let's say B is (2, 0), C is (3, 0) (so run is 3 - 2 = 1), and A is (3, 6) (so rise is 6 - 0 = 6). So rise = 6, run = 1, slope = 6/1 = 6.

Step2: Wait, maybe the grid is different. Let's check the vertical and horizontal. For a right triangle, rise is the vertical change (upwards), run is horizontal change (rightwards). So in triangle ABC, the vertical segment (rise) and horizontal segment (run). Let's count the units. If from B to C is 1 unit (run), and from C to A is 6 units (rise), then rise = 6, run = 1, slope = 6/1 = 6.

Answer:

(for part a, assuming the above):
rise: 6, run: 1, slope: 6

(Note: For part b, similar approach: find vertical change (rise) and horizontal change (run) for triangle DEF, then slope = rise/run. But since the graph is a bit unclear, but following the pattern, if DEF has E and F horizontal, then rise is vertical from E to D, run is horizontal from E to F. Suppose E is (4, 6), F is (5, 6) (run 1), D is (5, 18) (rise 18 - 6 = 12). Then rise = 12, run = 1, slope = 12/1 = 12? Wait, no, maybe the run is 2? Wait, maybe the grid has E at (4,6), F at (6,6) (run 2), and D at (6, 18) (rise 18 - 6 = 12). Then rise = 12, run = 2, slope = 12/2 = 6. Ah, that makes sense, same slope as ABC, since it's the same line. So for DEF, rise = 12, run = 2, slope = 6. But the initial part a: let's recheck. If ABC: B at (2,0), C at (3,0) (run 1), A at (3,6) (rise 6) → slope 6. DEF: E at (4,6), F at (6,6) (run 2), D at (6, 18) (rise 12) → slope 12/2 = 6. So for part a: rise = 6, run = 1, slope = 6. For part b: rise = 12, run = 2, slope = 6.)