Question

Graph the inequality on the axes below.
minus, 5, x, plus, 2, y, is greater than, minus, 8
−5x+2y>−8
Can you pls tell me the 2 points also they have to intercept the line so were the points on the lines are i need points outside it that go through them and pls tell me witch side is getting shaded


The points are based on the ineguality and slope

Answer 1

To graph the inequality \(-5x + 2y > -8\), let's first rewrite it in the slope-intercept form \(y = mx + b\) to easily identify the line and the points.

### Step 1: Rewrite the inequality

\[
-5x + 2y > -8
\]

Adding \(5x\) to both sides:

\[
2y > 5x - 8
\]

Now, divide everything by \(2\):

\[
y > \frac{5}{2}x - 4
\]

### Step 2: Identify the line and intercepts

Now, we can find the intercepts.

1. **Y-intercept**: Set \(x = 0\) in the equation \(y = \frac{5}{2}x - 4\):

\[
y = \frac{5}{2}(0) - 4 = -4
\]
So, the y-intercept is at the point \((0, -4)\).

2. **X-intercept**: Set \(y = 0\) in the equation \(y = \frac{5}{2}x - 4\):

\[
0 = \frac{5}{2}x - 4
\]

Adding \(4\) to both sides:

\[
\frac{5}{2}x = 4
\]

Multiply both sides by \(\frac{2}{5}\):

\[
x = \frac{8}{5} = 1.6
\]
So, the x-intercept is at the point \((1.6, 0)\).

We could summarize the intercept points:
- Y-intercept: \( (0, -4) \)
- X-intercept: \( (1.6, 0) \)

### Step 3: Graph the line

Now, we will graph the line based on these intercepts. Since the inequality is \(>\), we will draw a dashed line to indicate that points on the line are **not** included in the solution.

**Graph**:
1. Plot points \((0, -4)\) and \((1.6, 0)\) on a coordinate plane.
2. Draw a dashed line through these points.

### Step 4: Determine which side to shade

To determine which side of the line to shade, choose a test point not on the line. The point \((0, 0)\) is simple for testing:

Substituting into the original inequality:

\[
-5(0) + 2(0) > -8
\]
\[
0 > -8
\]
This is true, so we shade the side of the line that includes the point \((0, 0)\).

### Summary of the points
- **X-intercept**: \((1.6, 0)\)
- **Y-intercept**: \((0, -4)\)

### Shading
The side of the line where \((0, 0)\) is located (above the line) is shaded.