Question

2Which is the equation of a line that has a slope of -2/3 and passes through point(-3,-1)?o y=-x+1o y--3x+3o y=-2 / 8x-1o y=-2 /2x-3

Answer 1

Given:

The slope of the line, m=-2/3.

The coordinates of the point through which the line passes, (x1, y1)=(-3,-1).

The point-slope formula for the equation of a line can be written as,

`y-y1=m(x-x1)`

Now, substitute the known values.

`\begin{gathered} y-(-1)=(-2)/(3)(x-(-3) \\ y+1=(-2)/(3)(x+3) \end{gathered}`
`\begin{gathered} y+1=(-2)/(3)x-(2)/(3)*3 \\ y+1=(-2)/(3)x-2 \\ y=(-2)/(3)x-2-1 \\ y=(-2)/(3)x-3 \end{gathered}`

Therefore, the equation of the line is,

`y=-(2)/(3)x-3`