The equation of the line which passes through (1, 2) and is parallel to the line passing through (3, 4) and (4, 5), is:

Concept:

Straight Lines:

• The general equation of a line is y = mx + c, where m is the slope of the line.
• Parallel Lines: If two lines are parallel, then their slopes are equal.

Calculation:

Let the equation of the line passing through (3, 4) and (4, 5) be y = mx + c.

∴ We must have:

4 = 3m + c        ...(1)

And, 5 = 4m + c        ...(2)

Subtracting (1) from (2), we get:

1 = m.

Let the equation of the line passing through the point (1, 2) be y = nx + d.

Since this line is parallel to the above line, we must have n = m = 1.

Also, 2 = 1(1) + d.

⇒ d = 1.

The required equation is, therefore:

y = x + 1.