The equation of a line through the point (1, 2) whose distance from the point `(3,1)` has the greatest value is (a)`y=2x` (b) `y=x+1` (c)`x+2y=5` (d) `y=3x-1`

Options

A. y=2x
B. y=x+1
C. x+2y=5
D. y=3x-1

Explanation

To find the equation of the line through the point (1, 2) that has the greatest distance from the point (3, 1), we can follow these steps:

### Step 1: Write the equation of the line
Let the equation of the line be in the slope-intercept form:
\[ y = mx + c \]
Since the line passes through the point (1, 2), we can substitute these coordinates into the equation:
\[ 2 = m(1) + c \]
This simplifies to:
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