When 3x + 2y = 16 meets the y-axis what is the acute angle between the two.
The line represented by 3x + 2y = 16 meets the y-axis at the point where the x-coordinate is 0.
This gives 0 + 2y = 16
=> y = 8
At the point y = 8, if we draw a line parallel to the x-axis, it would make an angle of 90 degrees with the y-axis. Also, the slope of a line is the tan of the angle it makes with the x-axis.
3x + 2y = 16 can be written in the slope intercept form as 2y = 16 - 3x
=> y = 8 - (3/2)x
The slope of the line is -3/2
This gives the acute angle made with the x-axis as 56.3 degrees. It is negative as the line is downward sloping.
The line makes the same angle with the line y = 8. As y = 8 is perpendicular to the y-axis and the given line makes an acute angle of 56.3 degrees with it, the acute angle made with the y-axis is 90 - 56.3 = 33.69 degrees.
The required acute angle made with the y-axis at the point of intersection is 33.69 degrees.