Question

-3v -7 less equal sign 2v + 8

Answer 1

y = 2x + 3

x y
-2
-1
0
1

Answer 2

is the graph linear or nonlinear
x y
1 -1
5 3
9 7
13 3

Answer 3

is the graph linear or nonlinear
x y
-2 4
-1 9
0 14
1 19

Answer 4

rewrite the equation in Ax + By = C form
use integers for ABC
y - 2 = 3 (x + 3)

Answer 5

find the slope and y-intercept of the line
y = 4x - 5

Answer 6

To solve the inequality \(-3v - 7 \leq 2v + 8\), follow these steps:

1. **Combine like terms**:
Start by isolating the variable term on one side. We can do this by adding \(3v\) to both sides:

\[
-3v + 3v - 7 \leq 2v + 3v + 8
\]

This simplifies to:

\[
-7 \leq 5v + 8
\]

2. **Isolate the variable**:
Next, we subtract \(8\) from both sides:

\[
-7 - 8 \leq 5v
\]

Simplifying that gives:

\[
-15 \leq 5v
\]

3. **Divide by 5**:
Now, divide both sides by \(5\):

\[
\frac{-15}{5} \leq v
\]

This simplifies to:

\[
-3 \leq v
\]

or equivalently:

\[
v \geq -3
\]

So, the solution to the inequality is:

\[
v \geq -3
\]

Answer 7

To find the corresponding \( y \) values for each \( x \) value using the equation \( y = 2x + 3 \), we can substitute the given \( x \) values into the equation:

1. For \( x = -2 \):
\[
y = 2(-2) + 3 = -4 + 3 = -1
\]

2. For \( x = -1 \):
\[
y = 2(-1) + 3 = -2 + 3 = 1
\]

3. For \( x = 0 \):
\[
y = 2(0) + 3 = 0 + 3 = 3
\]

4. For \( x = 1 \):
\[
y = 2(1) + 3 = 2 + 3 = 5
\]

Now, we can summarize the results in a table:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & -1 \\
-1 & 1 \\
0 & 3 \\
1 & 5 \\
\hline
\end{array}
\]

So the corresponding \( y \) values for the given \( x \) values are:
- For \( x = -2 \), \( y = -1 \)
- For \( x = -1 \), \( y = 1 \)
- For \( x = 0 \), \( y = 3 \)
- For \( x = 1 \), \( y = 5 \)

Answer 8

To determine if the relationship between \( x \) and \( y \) is linear or nonlinear, we can check if the change in \( y \) is consistent with the change in \( x \).

Given the points:
- \( (1, -1) \)
- \( (5, 3) \)
- \( (9, 7) \)
- \( (13, 3) \)

### Step 1: Calculate the slopes between each pair of points

1. **Between (1, -1) and (5, 3)**:
\[
\text{slope} = \frac{3 - (-1)}{5 - 1} = \frac{3 + 1}{4} = \frac{4}{4} = 1
\]

2. **Between (5, 3) and (9, 7)**:
\[
\text{slope} = \frac{7 - 3}{9 - 5} = \frac{4}{4} = 1
\]

3. **Between (9, 7) and (13, 3)**:
\[
\text{slope} = \frac{3 - 7}{13 - 9} = \frac{-4}{4} = -1
\]

### Step 2: Analyze the slopes

The slope between the first two points is \(1\), and the slope between the second and third points is also \(1\), indicating that these segments are linear. However, the slope between the last two points is \(-1\), which indicates a change in direction.

### Conclusion

Since the slopes between the points are not consistent (they change between the third and fourth points), the relationship between \( x \) and \( y \) is **nonlinear**. The graph formed by these points will not be a straight line, as the direction of change in \( y \) does not remain constant.

Answer 9

To determine whether the relationship between \( x \) and \( y \) is linear or nonlinear, we'll check the slopes between each pair of points.

Given the points:
- \( (-2, 4) \)
- \( (-1, 9) \)
- \( (0, 14) \)
- \( (1, 19) \)

### Step 1: Calculate the slopes between each pair of consecutive points

1. **Between (-2, 4) and (-1, 9)**:
\[
\text{slope} = \frac{9 - 4}{-1 - (-2)} = \frac{5}{1} = 5
\]

2. **Between (-1, 9) and (0, 14)**:
\[
\text{slope} = \frac{14 - 9}{0 - (-1)} = \frac{5}{1} = 5
\]

3. **Between (0, 14) and (1, 19)**:
\[
\text{slope} = \frac{19 - 14}{1 - 0} = \frac{5}{1} = 5
\]

### Step 2: Analyze the slopes

The slopes between each pair of consecutive points are all equal to \( 5 \). This indicates that the relationship between \( x \) and \( y \) is consistent throughout the entire set of points.

### Conclusion

Since the slopes between all pairs of points are the same, the relationship between \( x \) and \( y \) is **linear**. The graph formed by these points will be a straight line.

Answer 10

To rewrite the equation \( y - 2 = 3(x + 3) \) in the form \( Ax + By = C \) using integers for \( A \), \( B \), and \( C \), we can follow these steps:

1. **Distribute** the \( 3 \) on the right side:
\[
y - 2 = 3x + 9
\]

2. **Add \( 2 \)** to both sides to isolate \( y \):
\[
y = 3x + 9 + 2
\]
\[
y = 3x + 11
\]

3. **Rearrange** the equation to the form \( Ax + By = C \) by moving all terms to one side:
\[
-3x + y = 11
\]

4. To express it in standard form, we prefer \( A \) to be positive, so we can multiply the entire equation by \(-1\):
\[
3x - y = -11
\]

Now, in the form \( Ax + By = C \), we have:
\[
3x - y = -11
\]

### Summary
In standard form \( Ax + By = C \), the integers are:
- \( A = 3 \)
- \( B = -1 \)
- \( C = -11 \)

Thus, the equation \( y - 2 = 3(x + 3) \) can be rewritten as \( 3x - y = -11 \).

Answer 11

The given equation of the line is:

\[
y = 4x - 5
\]

This equation is already in the slope-intercept form, which has the general form:

\[
y = mx + b
\]

where:
- \( m \) is the slope
- \( b \) is the y-intercept

### Identifying the Slope and Y-Intercept:

1. **Slope (\( m \))**: From the equation \( y = 4x - 5 \), we can see that the slope is \( 4 \).

2. **Y-Intercept (\( b \))**: The y-intercept is the value of \( y \) when \( x = 0 \). In this equation, the y-intercept is \( -5 \).

### Summary:

- **Slope**: \( 4 \)
- **Y-Intercept**: \( -5 \)

Thus, the slope of the line is \( 4 \) and the y-intercept is \( -5 \).