Question

What is the equation for the points (-3,1) and (-1,-1)

Answer 1

We need the equation for the line going through the points (-3, 1) and (-1, -1).

To do this we write the equation of the line as:

`y=mx+b`

The slope m can be calculated as the ratio of the difference of the y-coordinates and the difference of the x-coordinates:

`m=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1)=((-1)-1)/((-1)-(-3))=(-2)/(2)=-1`

Knowing the slope, we can calculate the y-intercept b using one of the points and replacing in the equation:

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

The equation of the line is: y=-x-2