What is the inclination of the line that passes through the points (8,2) and (12,6)?
The slope of a line passing through the points (x1, y1) and (x2, y2) is given by (y2 - y1)/(x2 - x1). The inclination of a line with the positive x axis is the arc tan of the slope.
Here we have the points (8, 2) and (12, 6)
The slope is (6 - 2)/(12 - 8) = 4/4 = 1
The slope of the line is 1.
The angle of inclination is arc tan 1 = pi/4
The required inclination of the line with the positive x-axis is pi/4.
Inclination of the line is the angle made by the line to x axis.
The inclination of the line depends on the gradient of that line.
The gradient of the line is the ratio between the changes in y direction and changes in x direction.
The inclination of the line is the slope of that line.
m = (y2 - y1)/(x2 - x1)
We notice that the numerator and denominator represents the legs of a right triangle.
m = tan a, where a is the angle made by the line and x axis.
x1 = 8 and x2 = 12
y1 = 2 and y2 = 6
tan a = (6 - 2)/(12 - 8)
tan a = 4/4
tan a = 1
The inclination of the line with respect to x axis is the angle a = pi/4 or 45 degrees.