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find the equation of the line if inсlіnаtіоn 120°, у-intercept equal to - 6

Sagot :

The inclination is the angle of the line with respect to x-axis:

in our case, angle alpha is equal to 120 degrees:

[tex]\alpha=120[/tex]

The slope m in the line equation

[tex]y=mx+b[/tex]

is related to alpha by the tangent function, that is

[tex]m=\text{tan }\alpha[/tex]

In our case, we have

[tex]\begin{gathered} m=\text{tan 120} \\ \sin ce\text{ tan120=-}\sqrt[]{3,}\text{ it yields} \\ m=-\sqrt[]{3} \end{gathered}[/tex]

So, our line equation has the form:

[tex]y=-\sqrt[]{3}x+b[/tex]

where b is the y-intercept, which is equal to -6.

Finally, the line equation is

[tex]y=-\sqrt[]{3}x-6[/tex]

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