The line passing through point (-3, 1) and point (x, 5) is parallel to the line passing through point (-2, -1) and point (6, 3). What is the value of x?

Solution (By Examveda Team)

Slope (m₁) for the line which passes through the points (-3, 1) and (x, 5) $$ = \frac{{5 - 1}}{{x + 3}} = \frac{4}{{x + 3}}$$
Similarly, slope (m₂) for the line which passes through the points (-2, -1) and (6, 3) $$ = \frac{{3 + 1}}{{6 + 2}} = \frac{4}{8} = \frac{1}{2}$$
If two lines are parallel to each other.
$$\eqalign{ & {\text{Then, }}{m_1} = {m_2} \cr & \Rightarrow \frac{4}{{x + 3}} = \frac{1}{2} \cr & \Rightarrow x + 3 = 8 \cr & \Rightarrow x = 5 \cr} $$