Question

right triangles abc and def are drawn to measure the slope of the line.
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.
rise:
run:
slope:

Explanation:

Part (a) - Triangle ABC

Step 1: Find Rise (Vertical Change)

Rise is the difference in y - coordinates. Point B is at (0, 5) (assuming from the graph, B is on y - axis with y = 5) and point C is at (6, 8). So rise = \(8 - 5=3\) (or looking at the vertical segment of triangle ABC, the vertical change from B to C is 3 units).

Step 2: Find Run (Horizontal Change)

Run is the difference in x - coordinates. The x - coordinate of B is 0 and of A (or D related to C) is 6. So run=\(6 - 0 = 6\) (horizontal segment from B to A is 6 units).

Step 3: Calculate Slope

Slope is defined as \(\frac{\text{rise}}{\text{run}}\). So slope=\(\frac{3}{6}=\frac{1}{2}\).

Part (b) - Triangle DEF

Step 1: Find Rise (Vertical Change)

Looking at triangle DEF, the vertical segment (rise) is smaller. Let's assume point E is at (2, 5) and point F is at (4, 6). Rise=\(6 - 5 = 1\) (vertical change from E to F is 1 unit).

Step 2: Find Run (Horizontal Change)

The horizontal segment (run) from E to D (or related x - change) is from x = 2 to x = 4. So run=\(4 - 2=2\).

Step 3: Calculate Slope

Slope=\(\frac{\text{rise}}{\text{run}}=\frac{1}{2}\).

Answer:

(a)

rise: \(3\)
run: \(6\)
slope: \(\frac{1}{2}\)

(b)

rise: \(1\)
run: \(2\)
slope: \(\frac{1}{2}\)