Question

Question 1

Show how to evaluate the equation for x = 2 and x = 5. Without simplifying first plug in the x values, then evaluate.

y = 5 + 3x - 7 - 2x

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

Answer 1

Question 2

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

y = 5 + 3x - 7 - 2x

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

Answer 2

Question 3

Use the slope intercept form of the equation from question 2 to evaluate the equation at x = 2 and x = 5.

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

Answer 3

Question 4

Are the results from question 1 and question 3 the same?

(1 point)
Responses

Yes.
Yes.

No..........

Answer 4

To evaluate the equation \(y = 5 + 3x - 7 - 2x\) for \(x = 2\) and \(x = 5\), we will follow the steps below:

### Step 1: Plug in \(x = 2\)

1. Substitute \(2\) in place of \(x\) in the equation:

\[
y = 5 + 3(2) - 7 - 2(2)
\]

2. Leave the expression unsimplified for now:

\[
y = 5 + 3 \cdot 2 - 7 - 2 \cdot 2
\]

### Step 2: Evaluate the expression for \(x = 2\)

Now simplify step-by-step:

- \(3 \cdot 2 = 6\)
- \(2 \cdot 2 = 4\)

Putting this back into the equation:

\[
y = 5 + 6 - 7 - 4
\]

Now, combine these values:

\[
y = 5 + 6 - 7 - 4 = 5 + 6 = 11
\]
\[
y = 11 - 7 = 4
\]
\[
y = 4 - 4 = 0
\]

Thus, the value of \(y\) when \(x = 2\) is:

\[
y = 0
\]

### Step 3: Plug in \(x = 5\)

1. Substitute \(5\) in place of \(x\) in the equation:

\[
y = 5 + 3(5) - 7 - 2(5)
\]

2. Leave the expression unsimplified for now:

\[
y = 5 + 3 \cdot 5 - 7 - 2 \cdot 5
\]

### Step 4: Evaluate the expression for \(x = 5\)

Now simplify step-by-step:

- \(3 \cdot 5 = 15\)
- \(2 \cdot 5 = 10\)

Putting this back into the equation:

\[
y = 5 + 15 - 7 - 10
\]

Now, combine these values:

\[
y = 5 + 15 = 20
\]
\[
y = 20 - 7 = 13
\]
\[
y = 13 - 10 = 3
\]

Thus, the value of \(y\) when \(x = 5\) is:

\[
y = 3
\]

### Final Results

For \(x = 2\), \(y = 0\).
For \(x = 5\), \(y = 3\).

Answer 5

To simplify the equation \(y = 5 + 3x - 7 - 2x\) and write it in slope-intercept form \(y = mx + b\), follow these steps:

### Step 1: Combine like terms

1. Start with the original equation:

\[
y = 5 + 3x - 7 - 2x
\]

2. Combine the constant terms \(5\) and \(-7\):

\[
5 - 7 = -2
\]

3. Combine the \(x\) terms \(3x\) and \(-2x\):

\[
3x - 2x = 1x \quad \text{or just} \quad x
\]

### Step 2: Rewrite the equation

Putting it all together, we have:

\[
y = x - 2
\]

### Step 3: Identify the slope and y-intercept

In the slope-intercept form \(y = mx + b\):

- \(m\) (slope) = 1
- \(b\) (y-intercept) = -2

### Final Result

The simplified equation in slope-intercept form is:

\[
y = x - 2
\]

Answer 6

To evaluate the equation \(y = x - 2\) at \(x = 2\) and \(x = 5\), we will plug in the values of \(x\) into the equation and calculate \(y\).

### Step 1: Evaluate at \(x = 2\)

1. Substitute \(2\) in place of \(x\):

\[
y = 2 - 2
\]

2. Calculate:

\[
y = 0
\]

Thus, when \(x = 2\), \(y = 0\).

### Step 2: Evaluate at \(x = 5\)

1. Substitute \(5\) in place of \(x\):

\[
y = 5 - 2
\]

2. Calculate:

\[
y = 3
\]

Thus, when \(x = 5\), \(y = 3\).

### Final Results

- For \(x = 2\), \(y = 0\).
- For \(x = 5\), \(y = 3\).

Answer 7

The results from Question 1 and Question 3 are as follows:

- From Question 1:
- For \(x = 2\), \(y = 0\)
- For \(x = 5\), \(y = 3\)

- From Question 3:
- For \(x = 2\), \(y = 0\)
- For \(x = 5\), \(y = 3\)

Since both sets of results are the same, the answer to the question is:

**Yes.**