Question

gabriel is going to get cable service for his home. the graph shows the cost of a cable plan, including installation fees. step 1 determine whether each statement is true or false. the lines slope between point a and point b is 25. select the lines slope between point b and point c is 50. select the lines slope between point a and point c is 50. select gabriels cable service will cost $50 each month. select reset step fast track

Explanation:

To solve this, we use the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \) and analyze each statement:

1. The line’s slope between point A and point B is 25.

• Point A: \( (2, 100) \), Point B: \( (4, 150) \)
• Slope: \( \frac{150 - 100}{4 - 2} = \frac{50}{2} = 25 \)
• True

2. The line’s slope between point B and point C is 50.

• Point B: \( (4, 150) \), Point C: \( (6, 200) \)
• Slope: \( \frac{200 - 150}{6 - 4} = \frac{50}{2} = 25 \) (not 50)
• False

3. The line’s slope between point A and point C is 50.

• Point A: \( (2, 100) \), Point C: \( (6, 200) \)
• Slope: \( \frac{200 - 100}{6 - 2} = \frac{100}{4} = 25 \) (not 50)
• False

4. Gabriel’s cable service will cost $50 each month.

• The slope represents the monthly cost (rate of change). From earlier, the slope is 25 (not 50).
• False

Final Answers:

1. The line’s slope between point A and point B is 25: \(\boldsymbol{\text{True}}\)
2. The line’s slope between point B and point C is 50: \(\boldsymbol{\text{False}}\)
3. The line’s slope between point A and point C is 50: \(\boldsymbol{\text{False}}\)
4. Gabriel’s cable service will cost $50 each month: \(\boldsymbol{\text{False}}\)

Answer:

To solve this, we use the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \) and analyze each statement:

1. The line’s slope between point A and point B is 25.

• Point A: \( (2, 100) \), Point B: \( (4, 150) \)
• Slope: \( \frac{150 - 100}{4 - 2} = \frac{50}{2} = 25 \)
• True

2. The line’s slope between point B and point C is 50.

• Point B: \( (4, 150) \), Point C: \( (6, 200) \)
• Slope: \( \frac{200 - 150}{6 - 4} = \frac{50}{2} = 25 \) (not 50)
• False

3. The line’s slope between point A and point C is 50.

• Point A: \( (2, 100) \), Point C: \( (6, 200) \)
• Slope: \( \frac{200 - 100}{6 - 2} = \frac{100}{4} = 25 \) (not 50)
• False

4. Gabriel’s cable service will cost $50 each month.

• The slope represents the monthly cost (rate of change). From earlier, the slope is 25 (not 50).
• False

Final Answers:

1. The line’s slope between point A and point B is 25: \(\boldsymbol{\text{True}}\)
2. The line’s slope between point B and point C is 50: \(\boldsymbol{\text{False}}\)
3. The line’s slope between point A and point C is 50: \(\boldsymbol{\text{False}}\)
4. Gabriel’s cable service will cost $50 each month: \(\boldsymbol{\text{False}}\)