Question
Solver system of inequalities by graphing why it's greater than or equal to 1/4 x - 3
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the inequality **y ≥ (1/4)x - 3** by graphing, follow these steps:
### Step 1: Graph the line
1. **Identify the y-intercept**: The y-intercept of the line **y = (1/4)x - 3** occurs when **x = 0**.
- Plugging in **x = 0**, we get:
\[ y = (1/4)(0) - 3 = -3 \]
- So, the y-intercept is (0, -3).
2. **Identify another point**: To find another point on the line, choose a value for **x**. Let’s use **x = 4**.
- Plugging in **x = 4**:
\[ y = (1/4)(4) - 3 = 1 - 3 = -2 \]
- So, another point on the line is (4, -2).
3. **Draw the line**: Plot the points (0, -3) and (4, -2) on a graph. Draw a **solid line** through the points because the inequality includes equal to (≥).
### Step 2: Shade the appropriate region
- Since we need to find where **y is greater than or equal to (1/4)x - 3**, shade the area **above the line**. This area represents all the points (x, y) that satisfy the inequality.
### Graph Summary
- The line should be solid because it's **greater than or equal to**.
- The region above this line represents all the (x, y) pairs satisfying the inequality **y ≥ (1/4)x - 3**.
### Step 3: Interpretation
- Any point in the shaded area is a solution to the inequality. For example, the point (0, 0) (which is above the line) would satisfy the inequality, as would points like (4, 1), (5, 2), etc.
### Final Graph:
You should now have a graph with a solid line representing **y = (1/4)x - 3** and the area above the line shaded, indicating all the values of y that satisfy the original inequality.
### Step 1: Graph the line
1. **Identify the y-intercept**: The y-intercept of the line **y = (1/4)x - 3** occurs when **x = 0**.
- Plugging in **x = 0**, we get:
\[ y = (1/4)(0) - 3 = -3 \]
- So, the y-intercept is (0, -3).
2. **Identify another point**: To find another point on the line, choose a value for **x**. Let’s use **x = 4**.
- Plugging in **x = 4**:
\[ y = (1/4)(4) - 3 = 1 - 3 = -2 \]
- So, another point on the line is (4, -2).
3. **Draw the line**: Plot the points (0, -3) and (4, -2) on a graph. Draw a **solid line** through the points because the inequality includes equal to (≥).
### Step 2: Shade the appropriate region
- Since we need to find where **y is greater than or equal to (1/4)x - 3**, shade the area **above the line**. This area represents all the points (x, y) that satisfy the inequality.
### Graph Summary
- The line should be solid because it's **greater than or equal to**.
- The region above this line represents all the (x, y) pairs satisfying the inequality **y ≥ (1/4)x - 3**.
### Step 3: Interpretation
- Any point in the shaded area is a solution to the inequality. For example, the point (0, 0) (which is above the line) would satisfy the inequality, as would points like (4, 1), (5, 2), etc.
### Final Graph:
You should now have a graph with a solid line representing **y = (1/4)x - 3** and the area above the line shaded, indicating all the values of y that satisfy the original inequality.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.