Question

Graph the inequality on the axes below.
minus, 2, x, plus, 5, y, is less than, 25
−2x+5y<25
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

Answer 1

To graph the inequality \(-2x + 5y < 25\) and determine the intercepts and shading, follow these steps:

1. **Convert the inequality into an equation**:
\[
-2x + 5y = 25
\]

2. **Find the intercepts**:
- **x-intercept** (where \(y = 0\)):
\[
-2x + 5(0) = 25 \implies -2x = 25 \implies x = -\frac{25}{2} \quad \text{(or } -12.5\text{)}
\]
- **y-intercept** (where \(x = 0\)):
\[
-2(0) + 5y = 25 \implies 5y = 25 \implies y = 5
\]

3. **Plot the points**:
- The x-intercept is \((-12.5, 0)\).
- The y-intercept is \((0, 5)\).

4. **Draw the line**:
Since the inequality is \(<\) (not \(\leq\)), the line should be dashed, indicating that points on the line are not included in the solution.

5. **Determine which side to shade**:
You can test a point not on the line to see if it satisfies the inequality. A common choice is \((0, 0)\):
\[
-2(0) + 5(0) < 25 \implies 0 < 25 \quad \text{(True)}
\]
Since the test point \((0, 0)\) satisfies the inequality, you would shade the side of the line that contains this point.

6. **Conclusion**:
- The two points that lie on the line are \((-12.5, 0)\) and \((0, 5)\).
- The area that is shaded is the area below the dashed line (since \(-2x + 5y < 25\)).

You can now graph this on a coordinate plane, marking the dashed line and shading appropriately.