the equation of a straight line passing through p(3,4) and makes an inclination of 135 with x axis in clockwise direction. then the equation of line is
The slope of a line equals tan A, where A is the angle that the line makes with the x-axis
So the slope of your line is tan (-135°) = 1
then y = x + b
but (3,4) lies on it, ...
4 = 3 + b
b = 1
y = x + 1
or
x - y = -1
To find the equation of a line passing through point P(3,4) and making an inclination of 135 degrees with the x-axis in the clockwise direction, you can follow these steps:
Step 1: Determine the slope of the line.
The angle of inclination is given as 135 degrees. Since we are measuring the angle clockwise from the positive x-axis, we need to subtract it from 180 degrees (which is a straight angle). Thus, the angle in the counterclockwise direction from the positive x-axis is 180 - 135 = 45 degrees.
The slope of a line is commonly denoted by "m" and is equal to the tangent of the angle between the line and the x-axis. In this case, the slope m can be calculated as the tangent of 45 degrees.
m = tan(45)
Use the tangent function to find the value of m.
Step 2: Use the point-slope form of a line to write the equation.
The point-slope form of a line is given by:
y - y1 = m(x - x1)
where (x1, y1) is the given point on the line, and m is the slope.
Substituting the values of the point P(3,4) and the slope m into the point-slope form, we get:
y - 4 = m(x - 3)
Step 3: Simplify and write the equation in standard form.
To simplify the equation, distribute the value of m to the terms within the parentheses:
y - 4 = m*x - 3m
Now, rearrange the equation so that it is in the standard form (Ax + By + C = 0), where A, B, and C are constants:
y - m*x = -3m + 4
-Rewrite the equation to match the standard form:
m*x + y = 3m - 4
So, the equation of the line passing through point P(3,4) with an inclination of 135 degrees with the x-axis in the clockwise direction is m*x + y = 3m - 4.