Question

Q1.If slope of the line joining points P(k, O) and Q (-3, -2) is 2/7 then find k​

Answer 1

Step-by-step explanation:

The value of k is 4 if the slope of the line joining the points P(k, 0) and Q( - 3, - 2) is 2/7

Slope of a line joining (x₁, y₁), (x₂, y₂) is given by,

$m = \dfrac{y _2 -y _1}{x_2 -x _1}$

Given,

The Slope of the line joining the points P(k, 0) and Q( - 3, - 2) is 2/7

Slope of the line PQ is,

$\begin{gathered}m = \frac{ - 2 - 0}{ - 3 - k} \\ \\ m = \frac{2}{3 + k} \end{gathered}$

Given Slope = 2/7

$\begin{gathered} \frac{2}{7} = \frac{2}{3 + k} \\ \\ 7 = 3 + k \\ \\ k = 7 - 3 \\ \\ k = 4\end{gathered}$

Therefore, The value of k is 4.

Another method to solve :

The equation of line passing through (h, k) and slope m is,

⇒y - k = m ( h - x)

Given, Slope of line PQ is 2/7

⇒ m = 2/7

Also, points P(k, 0) and Q( - 3, - 2)

By Point - Slope form,

⇒ Equation of line PQ

⇒ y + 2 = 2/7 ( x + 3)

⇒ 7 ( y + 2) = 2 ( x + 3)

⇒ 7y + 14 = 2x + 6

⇒ 2x - 7y + 6 - 14 = 0

⇒ 2x - 7y - 8 = 0

Since, P lies on the line, it should satisfy the above equation.

P(k, 0) lies on 2x - 7y - 8 = 0

⇒ 2(k) - 7(0) - 8 = 0

⇒ 2k - 8 = 0

⇒ 2k = 8

⇒ k = 4

Therefore, The value of k is 4 .