Question

self assessment
reflect and respond 1.1

reflect and respond 1.1

question 1
exercise

exercise
create a linear equation in 2 or more variables
create a linear equation based on an experience in your everyday life. in this experience, a variable should depend on at least one other variable (the independent variable(s)). if your equation has 2 variables, graph it on the coordinate plane.

Explanation:

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<reasoning>

Identify the real-world scenario

We need to create a linear equation based on a daily life experience. Let's choose a common scenario: calculating the total cost of a streaming service subscription that has a flat monthly fee plus a charge per movie rented.

• Flat monthly fee: \$10
• Cost per movie rental: \$3

Define the variables

Let's define the variables for our scenario:

• Let \(x\) represent the number of movies rented in a month (the independent variable).
• Let \(y\) represent the total monthly cost in dollars (the dependent variable).

Formulate the linear equation

The total cost \(y\) is the sum of the flat fee and the cost of the rented movies:
\[y = 3x + 10\]
Here, \(y\) depends on the independent variable \(x\).

Determine key points for graphing

To graph the equation \(y = 3x + 10\), we find at least two points on the coordinate plane:

• If \(x = 0\) (no movies rented):

\[y = 3(0) + 10 = 10 \implies (0, 10)\]

• If \(x = 2\) (2 movies rented):

\[y = 3(2) + 10 = 16 \implies (2, 16)\]

• If \(x = 4\) (4 movies rented):

\[y = 3(4) + 10 = 22 \implies (4, 22)\]
</reasoning>

<answer>

Scenario

A streaming service costs a flat fee of \$10 per month, plus \$3 for each premium movie rented.

Variables

• \(x\): Number of premium movies rented (independent variable)
• \(y\): Total monthly cost in dollars (dependent variable)

Linear Equation

\[y = 3x + 10\]
</answer>

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"type": "point",
"params": [[0, 10]],
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"params": [
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"js": "3*x + 10",
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0,
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Answer:

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<reasoning>

Identify the real-world scenario

We need to create a linear equation based on a daily life experience. Let's choose a common scenario: calculating the total cost of a streaming service subscription that has a flat monthly fee plus a charge per movie rented.

• Flat monthly fee: \$10
• Cost per movie rental: \$3

Define the variables

Let's define the variables for our scenario:

• Let \(x\) represent the number of movies rented in a month (the independent variable).
• Let \(y\) represent the total monthly cost in dollars (the dependent variable).

Formulate the linear equation

The total cost \(y\) is the sum of the flat fee and the cost of the rented movies:
\[y = 3x + 10\]
Here, \(y\) depends on the independent variable \(x\).

Determine key points for graphing

To graph the equation \(y = 3x + 10\), we find at least two points on the coordinate plane:

• If \(x = 0\) (no movies rented):

\[y = 3(0) + 10 = 10 \implies (0, 10)\]

• If \(x = 2\) (2 movies rented):

\[y = 3(2) + 10 = 16 \implies (2, 16)\]

• If \(x = 4\) (4 movies rented):

\[y = 3(4) + 10 = 22 \implies (4, 22)\]
</reasoning>

<answer>

Scenario

A streaming service costs a flat fee of \$10 per month, plus \$3 for each premium movie rented.

Variables

• \(x\): Number of premium movies rented (independent variable)
• \(y\): Total monthly cost in dollars (dependent variable)

Linear Equation

\[y = 3x + 10\]
</answer>

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