Find the area between the line and the two axes. x - 2y = -6

We are given an equation of line x - 2y = -6.

We need to find the area between the line and the two axes.

In order to find the area, we need to graph the triangle first.

Let us find x and y-intercepts of the graph to graph it on coordinates axes.

In order to find x-intercept, we need to plug y=0.

Plugging y=0 in given equation, we get

x-2(0) =-6.

x-0=-6.

x=-6.

So, x-intercept = -6.

In order to find y-intercept, we need to plug x=0.

Plugging x=0 in given equation, we get

0-2y=-6.

-2y=-6.

Dividing both sides by -2, we get

y=3.

So, y-intercept is =3.

Let us graph now.

We can see from the graph, base of the triangle = 6 units and height of the triangle=3 units.

We know formula for area of a triangle.

Area =

Plugging values of base =6 and height =3 in above formula, we get

Area =

=

= 9 square units.

Therefore, area between the line x - 2y = -6 and the two axes is 9 square units.

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step-by-step explanation:

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