If a line passing through (3, k) and (2, 7) is parallel to the line passing through (−1, 4) and (0, 6), then what is the value of k?

 Given:

 A line passing through two points (3, k) and (2, 7) is parallel to line passing through two points (-1, 4) and (0, 6).

 Concept Used:

• Equation of the line passing through two points is given by y = mx + c {Here m = \(\frac{y_{2} -y_{1}}{x_{2} - x_{1}}\)}
• If two lines are parallel to each other than their slopes are equal, and they have different y- intercepts.

 Solution:

 We will apply the formula to find out slope of first line i.e.m₁ =\(\frac{y_2 - y_1}{x_2 - x_1}\)

 ⇒ m₁ = \(\frac{7 - k}{2 - 3}\)

 ⇒ m₁ = k - 7

 We will apply the same formula to find the slope of second line.

 ⇒ m₂ = \(\frac{6 - 4}{0 + 1}\)

 ⇒ m₂ = 2

 We know that m₁ = m₂ {since lines are parallel}

 ⇒ k - 7 = 2

 ⇒ k = 9

 \(\therefore\) option 4 is correct.