Find the value of y such that the line through the points (5, y) and (2, 3) is parallel to the line through the points (9, - 2) and (6, - 5) ?

CONCEPT:

The slope of a line is given by tan α and it is denoted by m.

i.e m = tan α, where α ≠ π/2 and it represents the angle which a given line makes with respect to the X – axis in the positive direction.

Note:

• Slope of X –axis or a line parallel to X – axis is : m = tan 0° = 0

• Slope of Y – axis or a line parallel to Y – axis is: m = tan π/2 = ∞

• The slope of the line joining the points (x1, y1) and (x2, y2) is: 

• If two lines are parallel then their slope is same.

CALCULATION:

Here, we have to find the value of y such that the line through the points (5, y) and (2, 3) is parallel to the line through the points (9, - 2) and (6, - 5)

Let's find the slope of the line  through the points (9, - 2) and (6, - 5)

As we know that, the slope of the line joining the points (x1, y1) and (x2, y2) is: 

Here, x1 = 9, y1 = - 2, x2 = 6, y2 = - 5.

⇒ 

∵ The line through the points (5, y) and (2, 3) is parallel to the line through the points (9, - 2) and (6, - 5)

So, the slope of the line through the points (5, y) and (2, 3) is also 1.

So, know x1 = 5, y1 = y, x2 = 2, y2 =  3 and m = 1.

⇒ 

⇒ - 3 = 3 - y

⇒ y = 6

Hence, option A is the correct answer.