Solution:

Let 1: k be the ratio in which x-axis divides the line segment joining (–4, –6) and (–1, 7).

Therefore,

x-coordinate is (-1 – 4k) / (k + 1)

y-coordinate is (7 – 6k) / (k + 1)

y coordinate = 0, as P lies on x-axis,

$\left( 7\text{ }\text{ }6k \right)\text{ }/\text{ }\left( k\text{ }+\text{ }1 \right)\text{ }=\text{ }0$

$7\text{ }\text{ }6k\text{ }=\text{ }0$

$k\text{ }=\text{ }6/7$

Now, the value of m₁ = 6 and m₂ = 7

Using section formula, we get,

$x\text{ }=\text{ }({{m}_{1}}{{x}_{2}}~+\text{ }{{m}_{2}}{{x}_{1}})/({{m}_{1}}~+\text{ }{{m}_{2}})$

$=\text{ }\left( 6\left( -1 \right)\text{ }+\text{ }7\left( -4 \right) \right)/\left( 6+7 \right)$

$=\text{ }\left( -6-28 \right)/13$

$=\text{ }-34/13$

So,

$y\text{ }=\text{ }\left( 6\left( 7 \right)\text{ }+\text{ }7\left( -6 \right) \right)/\left( 6+7 \right)$

$=\text{ }\left( 42-42 \right)/13$

$=\text{ }0$

As a result, the coordinates of P are (-34/13, 0)