What Is 4x+6y=48 and what is the general form and x intercept and y intercept and slope and factored form?

Given equation : 4x+6y=48.

The general form of the linear equation is ax + by = c.

The given equation is already in general form.

Let us find x-intercept.

Plugging y = 0 in given equation.

4x+6 (0) = 48.

4x + 0 = 48

4x = 48

Dividing both sides by 4, we get

4x/4 = 48/4

x = 12.

Therefore, x-intercept is (12,0).

Let us find y-intercept.

Plugging x = 0 in given equation.

4 (0) + 6y=48.

6y = 48

Dividing both sides by 6, we get

6y/6 = 48/6

y = 8.

Therefore, y-intercept is (0,8).

Let us convert given equation in slope-intercept form y=mx+b.

4x+6y=48

Subtracting 4x from both sides, we get

4x-4x+6y=48-4x

6y = - 4x+48

Dividing both sides by 6, we get

6y/6 = - 4x/6+48/6

y = - 2/3 x + 8.

Therefore, slope is - 2/3.

Let us find factored form now.

GCF of the given linear equation is 2.

Factoring out 2 in all term, we get

3 (2x+3y=24)

That is factored form.