Question 6

Question

y = 2(5 - 3x) - 6 + 9x

Show how to evaluate the equation for x = 3 and x = 11. Plug in the x values, then evaluate.

(2 points)................

Answer 1

To evaluate the equation \( y = 2(5 - 3x) - 6 + 9x \) for \( x = 3 \) and \( x = 11 \), we will substitute these values of \( x \) into the equation and simplify.

Step 1: Evaluate for \( x = 3 \)

1. Substitute \( x = 3 \) into the equation: \[ y = 2(5 - 3(3)) - 6 + 9(3) \]

2. Calculate \( 3(3) \): \[ 3(3) = 9 \]

3. Substitute into the equation: \[ y = 2(5 - 9) - 6 + 27 \]

4. Calculate \( 5 - 9 \): \[ 5 - 9 = -4 \]

5. Substitute into the equation: \[ y = 2(-4) - 6 + 27 \]

6. Calculate \( 2(-4) \): \[ 2(-4) = -8 \]

7. Substitute: \[ y = -8 - 6 + 27 \]

8. Calculate \( -8 - 6 \): \[ -8 - 6 = -14 \]

9. Substitute: \[ y = -14 + 27 \]

10. Finally, calculate: \[ -14 + 27 = 13 \]

So, when \( x = 3 \), \( y = 13 \).

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Step 2: Evaluate for \( x = 11 \)

1. Substitute \( x = 11 \) into the equation: \[ y = 2(5 - 3(11)) - 6 + 9(11) \]

2. Calculate \( 3(11) \): \[ 3(11) = 33 \]

3. Substitute into the equation: \[ y = 2(5 - 33) - 6 + 99 \]

4. Calculate \( 5 - 33 \): \[ 5 - 33 = -28 \]

5. Substitute: \[ y = 2(-28) - 6 + 99 \]

6. Calculate \( 2(-28) \): \[ 2(-28) = -56 \]

7. Substitute: \[ y = -56 - 6 + 99 \]

8. Calculate \( -56 - 6 \): \[ -56 - 6 = -62 \]

9. Substitute: \[ y = -62 + 99 \]

10. Finally, calculate: \[ -62 + 99 = 37 \]

So, when \( x = 11 \), \( y = 37 \).

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Summary:

• When \( x = 3 \), \( y = 13 \).
• When \( x = 11 \), \( y = 37 \).

Answer 2

Question 7

Simplify the equation and write in slope intercept form (y = mx + b).

y = 2(5 - 3x) - 6 + 9x

(2 points).........

Answer 3

To simplify the equation \( y = 2(5 - 3x) - 6 + 9x \) and write it in slope-intercept form ( \( y = mx + b \) ), follow these steps:

Step 1: Distribute the \( 2 \)

1. Start with the original equation: \[ y = 2(5 - 3x) - 6 + 9x \]

2. Distribute \( 2 \) to both \( 5 \) and \( -3x \): \[ y = 2 \cdot 5 - 2 \cdot 3x - 6 + 9x \] This simplifies to: \[ y = 10 - 6x - 6 + 9x \]

Step 2: Combine like terms

1. Combine the constant terms \( 10 \) and \( -6 \): \[ 10 - 6 = 4 \]

2. Combine the \( x \) terms \( -6x \) and \( 9x \): \[ -6x + 9x = 3x \]

3. Now, substitute back: \[ y = 4 + 3x \]

Step 3: Rearrange to slope-intercept form

1. Reorder the equation to match the slope-intercept form \( y = mx + b \): \[ y = 3x + 4 \]

Final Result

The equation simplified in slope-intercept form is: \[ y = 3x + 4 \]

Here, the slope \( m \) is \( 3 \) and the y-intercept \( b \) is \( 4 \).

Answer 4

Question 8

Use the slope intercept form of the equation to evaluate the equation at x = 3 and x = 11.

(2 points),....

Answer 5

We have the equation in slope-intercept form:

\[ y = 3x + 4 \]

Now we can evaluate this equation at \( x = 3 \) and \( x = 11 \).

Step 1: Evaluate for \( x = 3 \)

1. Substitute \( x = 3 \) into the equation: \[ y = 3(3) + 4 \]

2. Calculate \( 3(3) \): \[ 3(3) = 9 \]

3. Substitute back into the equation: \[ y = 9 + 4 \]

4. Finally, calculate: \[ y = 13 \]

So, when \( x = 3 \), \( y = 13 \).

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Step 2: Evaluate for \( x = 11 \)

1. Substitute \( x = 11 \) into the equation: \[ y = 3(11) + 4 \]

2. Calculate \( 3(11) \): \[ 3(11) = 33 \]

3. Substitute back into the equation: \[ y = 33 + 4 \]

4. Finally, calculate: \[ y = 37 \]

So, when \( x = 11 \), \( y = 37 \).

Summary of Results:

• When \( x = 3 \), \( y = 13 \).
• When \( x = 11 \), \( y = 37 \).

Answer 6

Are the results from question 6 and question 8 the same?

(1 point)
Responses

Yes.
Yes.,............

Answer 7

Yes, the results from Question 6 and Question 8 are the same.

• In both questions, when \( x = 3 \), \( y = 13 \).
• In both questions, when \( x = 11 \), \( y = 37 \).

Thus, the answer is:

Yes.