Question

What is the value of y so that the line through (3, y)  and (2, 7) is parallel to the line through (−1, 4) and (0, 6)?

Answer 1

Let m₁ be the slope of the line passing through (3, y)  and (2, 7) and m₂ be the slope of the line passing through (−1, 4) and (0, 6). 

$$\therefore m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{7-y}{2-3}=\frac{7-y}{-1}=y-7$$ and $$m_2=\frac{y_2-y_1}{x_2-x_1}=\frac{6-4}{0+1}=\frac{2}{1}=2$$

For both the lines to be parallel, we must have,

$$m_1=m_2$$

$$\Rightarrow y-7=2$$

$$\Rightarrow y=9$$

Hence, the value of y is 9.