Answered

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17.
with the line x - 3y - 2 = 0.
Find the equation of lines passing through the point (1,-4) and making an angle of 135º ​

Sagot :

absor201

Answer:

The equation of the line passing through the point (1,-4) and making an angle of 135º ​will be:

  • [tex]y=-x-3[/tex]

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:

  • [tex]y=-x-3[/tex]
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