Answer:
The equation of the line passing through the point (1,-4) and making an angle of 135º will be:
Step-by-step explanation:
Given the point (1, -4)
Given that the line makes an angle of 135º.
so
Slope = m = tan 135º = -1
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = -1 and the point (1,-4)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-\left(-4\right)=-1\cdot \left(x-1\right)[/tex]
[tex]y+4=-\left(x-1\right)[/tex]
subtract 4 from both sides
[tex]y+4-4=-\left(x-1\right)-4[/tex]
simplify
[tex]y=-x-3[/tex]
Therefore, the equation of the line passing through the point (1,-4) and making an angle of 135º will be:
