Answer:
To find the equation of a line passing through point P(2, 5) and making an angle of θ = 135 degrees with the positive x-axis, you can use the point-slope form of the equation of a line:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is the point (2, 5), and m is the slope of the line.
First, let's find the slope (m) using the given angle θ. The slope of a line making an angle θ with the positive x-axis can be found using the tangent function:
m = tan(θ)
In this case, θ = 135 degrees. You can convert it to radians because most trigonometric functions expect angle values in radians:
θ (in radians) = (135°/180°) * π = (3/4) * π
Now, find the slope:
m = tan(3π/4)
The tangent of 3π/4 is -1. So, the slope (m) is -1.
Now, you can use the point-slope form with the values of (x₁, y₁) and m:
y - 5 = -1(x - 2)
Now, simplify:
y - 5 = -x + 2
To get the slope-intercept form (y = mx + b), isolate y:
y = -x + 2 + 5
y = -x + 7
So, the equation of the line passing through point P(2, 5) and making an angle of 135 degrees with the positive x-axis in slope-intercept form is:
y = -x + 7