Question 1

Question

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

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 2

Question 2

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

y = 5 + 3x - 7 - 2x

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

Answer 3

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 4

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 5

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 6

Question 4

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

(1 point)
Responses

Yes.
Yes.

No..........

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.