Find the angle formed by the x-axis and line whose equation is by 6y-7x=22
To find the angle formed by the x-axis and a line, we need to determine the slope of the line. The slope can be determined by rearranging the equation into the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
We start by rearranging the equation:
6y - 7x = 22
6y = 7x + 22
y = (7/6)x + 11/3
Thus, the slope of the line is m = 7/6.
To find the angle formed by the x-axis and the line, we use the fact that the tangent of an angle is equal to the slope of the line. Therefore, we take the arctangent of the slope:
tan(theta) = m
theta = arctan(m)
theta = arctan(7/6)
Using a calculator to evaluate arctan(7/6), we get:
theta ≈ 53.13 degrees
Therefore, the angle formed by the x-axis and the line with equation 6y - 7x = 22 is approximately 53.13 degrees.