Question

Graph the inequality on the axes below.
2, x, minus, 5, y, is less than or equal to, minus, 10
2x−5y≤−10

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 \(2x - 5y \leq -10\), we first need to find the boundary line by setting the equation to an equality:

\[
2x - 5y = -10.
\]

### Step 1: Find the intercepts

1. **x-intercept**: Set \(y = 0\):

\[
2x - 5(0) = -10 \implies 2x = -10 \implies x = -5.
\]

So, the x-intercept is \((-5, 0)\).

2. **y-intercept**: Set \(x = 0\):

\[
2(0) - 5y = -10 \implies -5y = -10 \implies y = 2.
\]

So, the y-intercept is \((0, 2)\).

### Step 2: Plot the line

Now we can plot the line with these intercepts:

- The point \((-5, 0)\) on the x-axis.
- The point \((0, 2)\) on the y-axis.

### Step 3: Determine the line type

Since the inequality is "less than or equal to" (\(\leq\)), we will draw a solid line through the intercept points since points on the line are included in the solution set.

### Step 4: Find points to test the inequality

To determine which side of the line to shade, we can test a point not on the line. A common choice is the origin \((0, 0)\):

Substitute \(x = 0\) and \(y = 0\) into the original inequality:

\[
2(0) - 5(0) \leq -10 \implies 0 \leq -10.
\]

This statement is false, so we do **not** shade the region that includes \((0, 0)\). Therefore, we will shade the opposite side of the line.

### Step 5: Identify points outside the line

You can choose any points in the shaded region as \(x\) and \(y\) values are less than the line. Here are two examples of points:

1. Point \((-6, 0)\):

\[
2(-6) - 5(0) = -12 \leq -10 \quad \text{(True)}
\]

2. Point \((-5, 1)\):

\[
2(-5) - 5(1) = -10 - 5 = -15 \leq -10 \quad \text{(True)}
\]

### Conclusion

- The points you can use as examples are: **\((-6, 0)\) and \((-5, 1)\)**.
- The region below the line \(2x - 5y = -10\) will be shaded, as this represents the solution set of the inequality \(2x - 5y ≤ -10\).

Feel free to plot these points and the line on a graph to visualize the solution!