Question

What is the equation of the line joining the points (1, 3) and (2, 7)? Prove that if (x, y) is a point on this line, so is the point (x + 1, y + 4).

Answer 1

The equation of a line passing through points (x₁, y₁) and (x₂, y₂) is given by:

The equation of the line passing through points (1, 3) and (2, 7) is:

⇒ y − 3 = 4x − 4

⇒ y − 4x = −1

If (x, y) is a point on this line, then it must satisfy the above equation.

Similarly, if (x + 1, y + 4) is a point on this line, then it must also satisfy the above equation.

Putting the coordinates (x + 1, y + 4) in the above equation:

y + 4 − 4(x + 1) = −1

⇒ y + 4 − 4x − 4 = −1

⇒ y − 4x = −1

This equation is identical to the original equation.

So, the point (x + 1, y + 4) also lie on the line y − 4x = −1 as the point (x, y).