What is the equation of a line passing through the point (a, b) and having a slope of b?

Solution:

Given: Slope is b and point (x₁, y₁) is (a, b)

The general slope point form of a line with slope m through the point (a, b) is

y - y₁ = m(x - x₁) --- (1)

Where 'm' is the slope of the line

Substitute the values in (1)

y - b = b(x - a)

Divide both sides of the equations by b

(y - b)/b = b(x - a)/b

y/b - 1 = x - a

Now convert it into standard form

⇒ x - (1/b)y = a - 1

Therefore, the equation of a line is x - (1/b)y = a - 1.

What is the equation of a line passing through the point (a, b) and having a slope of b?

Summary:

The equation of a line passing through the point (a, b) and having a slope of b is x - (1/b)y = a - 1.