Find the equation of a line passing through (2,3) and (5,4)

Answer

To find the equation of the line passing through the points (2, 3) and (5, 4), we can follow these steps:

### Step 1: Identify the points
Let the first point be \( (x_1, y_1) = (2, 3) \) and the second point be \( (x_2, y_2) = (5, 4) \).

### Step 2: Use the point-slope form of the equation of a line
The point-slope form of the equation of a line is given by:
\[ y - y_1 = \frac{y_2 - y_1}{x_2 - x_1} (x - x_1) \]

### Step 3: Substitute the values into the equation
Substituting the values of \( (x_1, y_1) \) and \( (x_2, y_2) \):
\[ y - 3 = \frac{4 - 3}{5 - 2} (x - 2) \]
This simplifies to:
\[ y - 3 = \frac{1}{3} (x - 2) \]

### Step 4: Multiply both sides by 3 to eliminate the fraction
Multiply both sides by 3:
\[ 3(y - 3) = x - 2 \]
This expands to:
\[ 3y - 9 = x - 2 \]

### Step 5: Rearrange the equation
Rearranging the equation gives:
\[ x - 3y + 7 = 0 \]

### Final Equation
Thus, the equation of the line is:
\[ x - 3y + 7 = 0 \]

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