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 (x₁, y₁) and (x₂, y₂) is given by:

Slope (m) = (y₂ - y₁) / (x₂ - x₁)

So, (x₁, y₁) = (1, 1) and (x₂, y₂) = (4, -12)

Substitute the given point (x₁, y₁) = (1, 1) in the equation of a line,

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

Now, Substitute (x₁, y₁) and (x₂, y₂) 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.