Find the equation of the line passing through:
(0, 1) and (1, 2) 

Answer

To find the equation of the line passing through the points (0, 1) and (1, 2), we can follow these steps:

### Step 1: Identify the points
We have two points:
- Point 1: \( (x_1, y_1) = (0, 1) \)
- Point 2: \( (x_2, y_2) = (1, 2) \)

### Step 2: Calculate the slope (m)
The slope \( m \) of the line passing through two points is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the values from our points:
\[ m = \frac{2 - 1}{1 - 0} = \frac{1}{1} = 1 \]

### Step 3: Use the point-slope form of the equation
The point-slope form of the equation of a line is:
\[ y - y_1 = m(x - x_1) \]
Using point \( (0, 1) \) and the slope \( m = 1 \):
\[ y - 1 = 1(x - 0) \]

### Step 4: Simplify the equation
Now, simplify the equation:
\[ y - 1 = x \]
Adding 1 to both sides gives:
\[ y = x + 1 \]

### Final Equation
Thus, the equation of the line passing through the points (0, 1) and (1, 2) is:
\[ y = x + 1 \]

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