We have given coordinates of two lines (3, y) and (2, 7), (– 1, 4) and (0, 6) 

To Find: Value of y? 

The concept used: Slopes of the parallel line are always equal. 

The formula used: The slope of line = \(\frac{y_2-y_1}{x_2-x_1}\)

Now, The slope of the line whose coordinates are (3, y) and (2, 7). 

M₁ = \(\frac{7-y}{2-3}\)    …… (1) 

And, Now, The slope of the line whose coordinates are (– 1, 4) and (0, 6). 

M₂ = \(\frac{6-4}{0-(-1)}\)

M₂ =  \(\frac{2}{1}\)…… (2) 

On equating the equation (1) and (2), we get

\(\frac{7-y}{2-3}=\frac{2}{1}\)

7 – y = 2(– 1) 

– y = – 2 – 7 

Y = 9 

Hence, The value of y is 9.

Slope of the line segment passing through (3, y) and (2, 7),

m₁ = \(\frac{7 − y}{2 − 3}\) = y – 7

And slope of the line passing through (– 1, 4) and (0, 6)

m₂ = \(\frac{6 − 4}{0 + 1}\) = 2

Since, the lines are parallel,

So m₁ = m₂

⇒ y – 7 = 2

⇒ y = 9