Question

What is the slope of the linear function given the following table?

х у-3. 6 -2. 51/3-1. 42/30. 43. 2Help please !

Answer 1

Let's use two points of the table:

`\begin{gathered} (x1,y1)=(-1,3) \\ (x2,y2)=(0,1) \end{gathered}`

Let's find the slope using the following formula:

`m=(y2-y1)/(x2-x1)=(1-3)/(0-(-1))=-(2)/(1)=-2`

Using the point-slope equation:

`\begin{gathered} y-y1=m(x-x1) \\ y-3=-2(x+1) \\ y-3=-2x-2 \\ y=-2x+1 \end{gathered}`

-------------------------------------------------

For the 2nd table:

`\begin{gathered} (x1,y1)=(-3,6) \\ (x2,y2)=(0,4) \end{gathered}`

Let's find the slope:

`m=(4-6)/(0-(-3))=-(2)/(3)`

Using the point-slope equation:

`\begin{gathered} y-y1=m(x-x1) \\ y-6=-(2)/(3)(x+3) \\ y-6=-(2)/(3)x-2 \\ y=-(2)/(3)x+4 \end{gathered}`