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:
m= Here,
x1=9,y1=−2,x2=6,y2=−5 ⇒m==1 ∵ 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.
⇒1= ⇒−3=3−y ⇒y=6 Hence, option A is the correct answer.