Question

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

Answer 1

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

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

`\alpha=120`

The slope m in the line equation

`y=mx+b`

is related to alpha by the tangent function, that is

`m=\text{tan }\alpha`

In our case, we have

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

So, our line equation has the form:

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

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

Finally, the line equation is

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