Ask a New Question
Menu

Ryan is tracking how much money he has each week.

He started with $60.

He spent $5 per week for the first 6 weeks.

He spent $10 per week after week 6 until the money's all spent.

options:

The y-intercept for this scenario would be ______ area meaning ________

options:

(10,6)
Negative
(10,0)
Ryan started with $60 in his account
Ryan decreases his $ each week
(0,5)
Ryan took 10 weeks to spend all of his $
(0, 60)
Linear
(6,5)
Positive

5 answers

To address the scenario, we first analyze the parts:

  1. Ryan starts with $60.
  2. For the first 6 weeks, he spends $5 each week.
  3. After week 6, he spends $10 each week until his money is fully spent.

Let’s calculate how much money Ryan has after each period:

  • Weeks 1-6:

    • Money spent in 6 weeks: \( 6 \times 5 = 30 \)
    • Money remaining after 6 weeks: \( 60 - 30 = 30 \)

  • Weeks 7 and onward:

    • Starting with $30, and now he spends $10 per week.
    • Weeks needed to spend remaining $30: \( \frac{30}{10} = 3 \) weeks.

Total weeks spent before money is fully spent:

  • 6 weeks + 3 weeks = 9 weeks.

Now, looking at the provided options about the y-intercept:

The y-intercept in this context represents the starting amount of money Ryan had, which is $60. In a graph where the x-axis represents weeks and the y-axis represents money, the intercept would be at (0, 60).

Thus, the first option that matches the y-intercept is:

  • (0, 60)

The explanation for this option matches the statement that Ryan started with $60 in his account.

So the answer you are looking for is:

  • (0, 60)
  • Ryan started with $60 in his account.
The rate of change ________ because as the weeks increase, the money decreases.

options:

(10,6)
Negative
(10,0)
Ryan started with $60 in his account
Ryan decreases his $ each week
(0,5)
Ryan took 10 weeks to spend all of his $
(0, 60)
Linear
(6,5)
Positive

The statement "The rate of change ________ because as the weeks increase, the money decreases" indicates that the money Ryan has is decreasing as time goes on. This implies that the slope of the graph is negative.

Thus, the correct option to fill in the blank is:

  • Negative

So, the complete sentence would be: "The rate of change is negative because as the weeks increase, the money decreases."

The equation of Line 1: 4x - 2y = 16

The equation of Line 2: y = -4/5x + 2

The equation of Line 3: y - 4 = 3 (x + 5)

Which statement is true?

options:

Line 2 has an increasing graph
Line 2 has an increasing graph

Line 3 has the greatest slope
Line 3 has the greatest slope

Line 1 has the biggest y-intercept
Line 1 has the biggest y-intercept

Line 2 has the biggest y-intercept
Line 2 has the biggest y-intercept

Line 1 has the greatest slope.
Line 1 has the greatest slope.

Line 3 has a decreasing graph

Let's analyze the equations of the lines to determine their slopes and y-intercepts.

  1. Line 1: \(4x - 2y = 16\)

    To find the slope and y-intercept, we can rewrite this in slope-intercept form \(y = mx + b\): \[ -2y = -4x + 16 \ y = 2x - 8 \]

    • Slope (\(m\)) = 2
    • y-intercept (\(b\)) = -8

  2. Line 2: \(y = -\frac{4}{5}x + 2\)

    This is already in slope-intercept form:

    • Slope (\(m\)) = \(-\frac{4}{5}\)
    • y-intercept (\(b\)) = 2

  3. Line 3: \(y - 4 = 3(x + 5)\)

    We can expand this equation: \[ y - 4 = 3x + 15 \ y = 3x + 19 \]

    • Slope (\(m\)) = 3
    • y-intercept (\(b\)) = 19

Now, let's summarize the slopes and y-intercepts:

  • Line 1: Slope = 2, y-intercept = -8
  • Line 2: Slope = \(-\frac{4}{5}\), y-intercept = 2
  • Line 3: Slope = 3, y-intercept = 19

Now let's evaluate the options:

  1. Line 2 has an increasing graph - False (it has a negative slope).
  2. Line 3 has the greatest slope - True (Slope = 3, which is greater than the slopes of Lines 1 and 2).
  3. Line 1 has the biggest y-intercept - False (y-intercept of -8 is less than Line 2 and Line 3).
  4. Line 2 has the biggest y-intercept - False (Line 3 has the biggest y-intercept).
  5. Line 1 has the greatest slope - False (Line 3 has a greater slope).
  6. Line 3 has a decreasing graph - False (it has a positive slope).

The statement that is true is:

  • Line 3 has the greatest slope.