What is the size of the acute angle formed by the x axis and the line 3x+2y=12?

The crucial piece of information we’ll first need to find is the *slope* of the line. That slope is also the *tangent* of the angle formed by the x-axis and the line, so taking the arctangent of the slope will get us the angle.

To find the slope, we’ll need to find the change in y over the change in x - for that, we’ll need two points.

We can find those points by plugging in two values for x, and solving the equation for y. I’ll choose the values x = 0 and x = 2

Point A (x = 0):

3(0) + 2y = 12
2y = 12
y = 6

So we have A(0, 6)

Point B (x = 2)

3(2) + 2y = 12
6 + 2y = 12
2y = 6
y = 3

And we find B(2, 3)

So, our slope is (3-6)/(2-0) = -3/2

Taking arctan(-3/2) to find the angle, we find

arctan(-3/2) ~= -56.31 degrees, or positive 56.31 degrees, depending on where the angle is measured from.