complete the parts below.\n(a) find the rise, run, and slope given by triangle abc.\nrise: \nrun: \nslope…

Answer:

(a) rise: $1$, run: $4$, slope: $\frac{1}{4}$ (b) rise: $1$, run: $4$, slope: $\frac{1}{4}$

Explanation:

Step1: Determine the rise and run for triangle (ABC)

• Rise: The vertical change. From point (C) to (B), the vertical change is (1) unit (since (y) - value changes by (1)).
• Run: The horizontal change. From point (C) to (B), the horizontal change is (4) units (since (x) - value changes by (4)).
• Slope formula: (m=\frac{\text{rise}}{\text{run}}). Substituting rise ( = 1) and run (=4), we get (m = \frac{1}{4}).

Step2: Determine the rise and run for triangle (DEF)

• Rise: The vertical change. From point (F) to (E), the vertical change is (1) unit (since (y) - value changes by (1)).
• Run: The horizontal change. From point (F) to (E), the horizontal change is (4) units (since (x) - value changes by (4)).
• Slope formula: (m=\frac{\text{rise}}{\text{run}}). Substituting rise ( = 1) and run (=4), we get (m=\frac{1}{4}).

Since the slope of a line is constant (for a non - vertical line), the slopes of the two triangles (which are parts of the same line) are equal.