Question

What is the equation of the line that passes through the point (-5, -2) and has aslope of -6/5

Answer 1

The equation of the line is;

`y=-(6)/(5)x-8`

Step-by-step explanation:

Given the slope of the line as;

`m=-(6)/(5)`

And passes through point;

`(-5,-2)`

Using the Point-slope equation to derive the equation of the line;

`\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=-(6)/(5)(x-(-5)) \\ y+2=-(6)/(5)(x+5) \end{gathered}`

Simplifying;

`\begin{gathered} y+2=-(6)/(5)x-(6)/(5)(5) \\ y+2=-(6)/(5)x-6 \\ y=-(6)/(5)x-6-2 \\ y=-(6)/(5)x-8 \end{gathered}`

Therefore, the equation of the line is;

`y=-(6)/(5)x-8`