Question

Use the image to answer the question.

A coordinate plane shows four quadrants with both the axes ranging from negative 5 to 5 in unit increments. Two points are plotted, with a dashed line passing through them. The dashed line passes through two points marked at left parenthesis negative 2 comma 0 right parenthesis and left parenthesis 0 comma 4 right parenthesis. The line extends beyond both points. The area above the dashed line is shaded.

Given the graph for the solution set of an inequality, identify the coefficients for x
and y
in the inequality.

(1 point)
y>

x+8

Answer 1

no

Answer 2

To find the coefficients for \(x\) and \(y\) in the given inequality \(y > x + 8\) based on the graph described, we can analyze the points that the dashed line passes through.

The two points marked on the dashed line are \((-2, 0)\) and \((0, 4)\).

1. **Calculate the slope of the line**:
The slope \(m\) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Where \((x_1, y_1) = (-2, 0)\) and \((x_2, y_2) = (0, 4)\):
\[
m = \frac{4 - 0}{0 - (-2)} = \frac{4}{2} = 2
\]

2. **Use point-slope form to find the equation of the line**:
Using the point-slope form \(y - y_1 = m(x - x_1)\):
\[
y - 0 = 2(x + 2)
\]
This simplifies to:
\[
y = 2x + 4
\]

3. **Rearranging the equation**:
We can express this in the standard linear form:
\[
2x - y + 4 = 0
\]
Rearranging gives:
\[
-y = -2x - 4
\]
Flipping the signs:
\[
y = 2x + 4
\]

4. **Identifying the inequality**:
Since the area above the dashed line is shaded, the inequality is:
\[
y > 2x + 4
\]

Thus, the coefficients for \(x\) and \(y\) in the inequality are:

- Coefficient of \(x\) is \(2\)
- Coefficient of \(y\) is \(-1\) (since it is \(y - 2x - 4 > 0\))

Therefore, the complete answer is:

**Coefficients for \(x\) and \(y\) in the inequality:** \(y > 2x + 4\).

Answer 3

I apologize for any confusion. Let's start over and address the problem more clearly.

Based on your description, it seems the dashed line passes through the coordinates \((-2, 0)\) and \((0, 4)\).

1. **Equation of the Line**:
We first find the slope between the two points:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 0}{0 - (-2)} = \frac{4}{2} = 2.
\]

Now we use the point-slope form of the equation of a line:
\[
y - y_1 = m(x - x_1).
\]
Using point \((0, 4)\):
\[
y - 4 = 2(x - 0) \implies y = 2x + 4.
\]

2. **Rearranging the Equation**:
The equation in standard form is:
\[
-2x + y - 4 = 0 \implies 2x - y + 4 = 0 \implies y = 2x + 4.
\]

3. **Setting Up the Inequality**:
Since the area above the dashed line is shaded, we denote this as:
\[
y > 2x + 4.
\]

Based on the standard form of the line \(y = mx + b\), where \(m\) is the coefficient of \(x\), we find:

- Coefficient of \(x\) is \(2\),
- Coefficient of \(y\) when rearranged to the form \(Ax + By > C\) is \(-1\) (which comes from the rearranged equation \(2x - y + 4 > 0\)).

So the inequality can be rewritten to show coefficients explicitly:

### Answer:
The coefficients in the inequality \(y > 2x + 4\) are:
- Coefficient of \(x\): \(2\),
- Coefficient of \(y\): \(-1\).

If there are further specifics to clarify or adjust about my response or if you have another question, please let me know!