The graph of every linear eqution in two variables is a _______

Answer

To answer the question "The graph of every linear equation in two variables is a _______", we need to understand the characteristics of linear equations in two variables and how they are represented graphically.

### Step-by-Step Solution:

1. **Understanding Linear Equations**:
A linear equation in two variables can be expressed in the standard form:
\[ ax + by = c \]
where \(a\), \(b\), and \(c\) are constants, and \(x\) and \(y\) are the variables.

**Hint**: Recall that a linear equation represents a relationship between two variables.

2. **Finding Points for the Graph**:
To graph this equation, we need to find at least two points that satisfy the equation. We can do this by substituting values for \(x\) and solving for \(y\), and vice versa.

**Hint**: Choose simple values for \(x\) or \(y\) (like 0) to make calculations easier.

3. **Calculating Points**:
- **First Point**: Let’s set \(x = 0\):
\[ 0 + by = c \implies y = \frac{c}{b} \]
Thus, one point is \((0, \frac{c}{b})\).

- **Second Point**: Now, let’s set \(y = 0\):
\[ ax + 0 = c \implies x = \frac{c}{a} \]
Thus, another point is \((\frac{c}{a}, 0)\).

**Hint**: Finding points where either variable is zero is a common method to plot linear equations.

4. **Plotting the Points**:
On a graph, plot the points \((0, \frac{c}{b})\) and \((\frac{c}{a}, 0)\).

**Hint**: Make sure to label your axes correctly (x-axis and y-axis).

5. **Drawing the Line**:
After plotting the two points, draw a straight line through them. This line represents all the solutions to the linear equation.

**Hint**: A straight line indicates a linear relationship between the variables.

6. **Conclusion**:
The graph of every linear equation in two variables is a straight line.

**Final Answer**: The graph of every linear equation in two variables is a **straight line**.