Question

An expression is shown/

4(34x+3x−2)−2(3x2+1+3x)

Rewrite an equivalent expression with the fewest terms possible

(3 points)
x2
+
x−

Answer 1

An expression is shown/

4(3/4x+3x−2)−2(3x2+1+3x)

Rewrite an equivalent expression with the fewest terms possible

(3 points)

Answer 2

An equation is shown.

y−5 = −3(x+6)
(2 points)
The equation rewritten in slope-intercept form is
.

The point
is on the graph of the line.

Answer 3

y-5=-3(x+6)
slope intercept
the point

Answer 4

there is no 0,-13

Answer 5

Complete the statements.

The slope of the line is Response area
The y-intercept is Response area Write this as an ordered pair
An equation of the line in slope-intercept form is Response area
A point on the graph that is NOT the y-intercept is Response area
An equation of the line in point-slope form is Response area


Skip to navigation

Answer 6

Let's simplify the expression step by step.

Given expression:
\[ 4(34x + 3x - 2) - 2(3x^2 + 1 + 3x) \]

1. First, distribute the constants inside the parentheses:

\[
4(34x) + 4(3x) - 4(2) - 2(3x^2) - 2(1) - 2(3x)
\]

This becomes:

\[
136x + 12x - 8 - 6x^2 - 2 - 6x
\]

2. Now, combine like terms:

\[
-6x^2 + (136x + 12x - 6x) - 8 - 2
\]

Combine the \(x\) terms:

\[
-6x^2 + 142x - 10
\]

The simplified form of the expression is:

\[
-6x^2 + 142x - 10
\]

If you need it in the form specified in your question, let me know!

Answer 7

Let's simplify the given expression step by step:

**Given expression:**
\[
4\left(\frac{3}{4}x + 3x - 2\right) - 2(3x^2 + 1 + 3x)
\]

1. **Distribute the constants inside the parentheses:**

- For the first term:
\[
4\left(\frac{3}{4}x\right) = 3x
\]
\[
4(3x) = 12x
\]
\[
4(-2) = -8
\]
So, the first term becomes:
\[
3x + 12x - 8 = 15x - 8
\]

- For the second term:
\[
-2(3x^2) = -6x^2
\]
\[
-2(1) = -2
\]
\[
-2(3x) = -6x
\]
So, the second term becomes:
\[
-6x^2 - 6x - 2
\]

2. **Combine the two results:**
The entire expression now looks like this:
\[
(15x - 8) + (-6x^2 - 6x - 2)
\]

3. **Combine like terms:**
\[
-6x^2 + (15x - 6x) + (-8 - 2)
\]
Which simplifies to:
\[
-6x^2 + 9x - 10
\]

Thus, the equivalent expression with the fewest terms possible is:
\[
-6x^2 + 9x - 10
\]

Answer 8

To rewrite the equation \( y - 5 = -3(x + 6) \) in slope-intercept form (which is \( y = mx + b \)), we'll follow these steps:

1. **Distribute the \(-3\) on the right side:**

\[
y - 5 = -3x - 18
\]

2. **Add \(5\) to both sides to isolate \(y\):**

\[
y = -3x - 18 + 5
\]

\[
y = -3x - 13
\]

Now, the equation in slope-intercept form is:
\[
y = -3x - 13
\]

### Identifying a Point on the Graph:

To find a point on the graph of the line, we can choose any value for \(x\) and solve for \(y\).

Let's choose \(x = 0\):

1. Plug \(x = 0\) into the equation:
\[
y = -3(0) - 13 = -13
\]

Thus, the point \((0, -13)\) is on the graph of the line.

### Final Answers:

- The equation in slope-intercept form is:
\[
y = -3x - 13
\]

- The point that is on the graph of the line is:
\[
(0, -13)
\]

Answer 9

To rewrite the equation \( y - 5 = -3(x + 6) \) in slope-intercept form and find a point on the graph, follow these steps:

### Step 1: Rewrite in Slope-Intercept Form
Start with the given equation:
\[
y - 5 = -3(x + 6)
\]

1. **Distribute the \(-3\):**
\[
y - 5 = -3x - 18
\]

2. **Add \(5\) to both sides:**
\[
y = -3x - 18 + 5
\]
\[
y = -3x - 13
\]

### Slope-Intercept Form
The equation in slope-intercept form is:
\[
y = -3x - 13
\]
- **Slope (m):** \(-3\)
- **Y-intercept (b):** \(-13\)

### Step 2: Find a Point on the Graph
We can find a point by substituting a value for \(x\) into the equation.

**Let's choose \(x = 0\):**
\[
y = -3(0) - 13 = -13
\]
Thus, one point on the graph is:
\[
(0, -13)
\]

### Summary
- **Slope-Intercept Form:** \(y = -3x - 13\)
- **Point on the Graph:** \((0, -13)\)

Answer 10

I apologize for the oversight! Let's reassess the equation and calculate a suitable point accurately.

Given the equation:

\[
y - 5 = -3(x + 6)
\]

### Step 1: Rewrite in Slope-Intercept Form

1. **Distribute the \(-3\)**:

\[
y - 5 = -3x - 18
\]

2. **Add \(5\) to both sides**:

\[
y = -3x - 18 + 5
\]

\[
y = -3x - 13
\]

### Slope-Intercept Form
The equation in slope-intercept form is:
\[
y = -3x - 13
\]

- **Slope (m):** \(-3\)
- **Y-intercept (b):** \(-13\)

### Step 2: Find a Point on the Graph
Let's find a point by choosing a different value for \(x\).

**Let's choose \(x = -6\)** (a convenient choice because it simplifies our original equation):
\[
y = -3(-6) - 13
\]

Calculating it:
\[
y = 18 - 13 = 5
\]

Thus, we have the point:
\[
(-6, 5)
\]

### Summary
- **Slope-Intercept Form:** \(y = -3x - 13\)
- **Point on the Graph:** \((-6, 5)\)

Thank you for your patience! If you have further questions, feel free to ask!

Answer 11

Let's complete the statements based on the equation we derived earlier, which is:

\[
y = -3x - 13
\]

### Completing the Statements

1. **The slope of the line is:**
**Response area:** \(-3\)

2. **The y-intercept is:**
**Response area:** \(-13\)
(This can also be written as the ordered pair (0, -13).)

3. **Write this as an ordered pair:**
**Response area:** \((0, -13)\)

4. **A point on the graph that is NOT the y-intercept is:**
**Response area:** \((-6, 5)\)
(This is the point we found in the previous response.)

5. **An equation of the line in point-slope form is:**
The point-slope form is given by the formula:
\[ y - y_1 = m(x - x_1) \]
Using the point \((-6, 5)\) and the slope \(-3\):
**Response area:**
\[ y - 5 = -3(x + 6) \]
(This is equivalent to the form we started with.)

### Summary of Responses
1. The slope of the line is: **-3**
2. The y-intercept is: **-13**
3. Write this as an ordered pair: **(0, -13)**
4. A point on the graph that is NOT the y-intercept is: **(-6, 5)**
5. An equation of the line in point-slope form is: **y - 5 = -3(x + 6)**

Feel free to ask any further questions!