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# Find an equation of the line passing through the given points. (1, 1), (4, -12).

**Solution:**

From the question it is given that pair of points. (1, 1), (4, -12).

The slope of the line that passes through (x_{1}, y_{1}) and (x_{2}, y_{2}) is given by:

Slope (m) = (y_{2} - y_{1}) / (x_{2} - x_{1})

So, (x_{1}, y_{1}) = (1, 1) and (x_{2}, y_{2}) = (4, -12)

Substitute the given point (x_{1}, y_{1}) = (1, 1) in the equation of a line,

y - 1 = m (x - 1) --- (equation 1)

Now, Substitute (x_{1}, y_{1}) and (x_{2}, y_{2}) with their given values, we get,

m = (-12 - 1) / (4 - 1)

m = -13 / 3

Substituting value of m in (equation 1), we get

y - 1 = (-13/3)(x - 1)

3y - 3 = -13x + 13

3y = -13x + 16

y = (-13x + 16)/3

Therefore, the equation of the line is y = (-13x + 16)/3.

## Find an equation of the line passing through the given points. (1, 1), (4, -12).

**Summary:**

The equation of the line passing through the given points. (1, 1), (4, -12) is y = (-13x + 16)/3.

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