Write an equation of the line in a point-slope form that passes through the two given points.

We will use the concept of the equation of a straight line in order to find the equation of the line.

Answer: y = [(b - d) (x - a) / (a - c)] + b is the required line that passes through points (a, b) and (c, d).

Let us see how we will use the concept of the equation of a straight line in order to find the equation of the line.

Explanation:

Let us consider two points (a, b) and (c, d) through which our required line passes.

Now let us consider another point (x, y) through which our line passes.

From the mathematical definition of slope that is,

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

(y - b) (a - c) = (b - d) (x - a)

From the above equation, we have to calculate the value of y,

(y - b) = (b - d) (x - a) / (a - c)

y = [(b - d) (x - a) / (a - c)] + b

Thus, y = [(b - d) (x - a) / (a - c)] + b is the required line that passes through points (a, b) and (c, d).