Question

1. the slope of the line defined by the equation 2x + 3y - 6 is: a. 3/2 b. 2/3 c - 2/3 d - 3/2 17. based on the vertical angles conjecture, if ∠aec = 45°, what is the measure of ∠bed? a. 45° b. 30° c. 60° d. 70° 18. which proof method is best for complex proofs with multiple branches? a. indirect proof b. two - column proof c. flowchart proof d. paragraph proof

Explanation:

Step1: Rewrite line equation in slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope. Given $2x+3y - 6=0$, solve for $y$. First, isolate $y$: $3y=-2x + 6$, then $y=-\frac{2}{3}x+2$. The slope $m =-\frac{2}{3}$.

Step2: Recall vertical - angles property

Vertical angles are congruent. If $\angle AEC = 45^{\circ}$, and $\angle AEC$ and $\angle BED$ are vertical angles, then $\angle BED=\angle AEC = 45^{\circ}$.

Step3: Analyze proof - methods

For complex proofs with multiple branches, a flowchart proof is the best as it can clearly show the logical flow and different branches of the proof.

Answer:

1. d. $-\frac{2}{3}$
2. a. $45^{\circ}$
3. c. Flowchart proof