Question

Question 6

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

---

### 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 \( x = 11 \), \( y = 37 \).

---

### 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 \( x = 3 \), \( y = 13 \).

---

### 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.**