Question

what is the slope-intercept form of the function described by this tableX- 1, 2, 3, 4Y- -2 -6, -10 -14

Answer 1

Let's begin by listing out the information given to us:

`(x,y)=(1,-2),(2,-6),(3,-10),(4,-14)`

The slope-intercept form is given by:

`\begin{gathered} y=mx+b \\ where\colon m=slope,b=y-intercept \end{gathered}`

The slope is calculated by picking any two ordered pairs or coordinates and substituted into the slope formula:

`\begin{gathered} m=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1) \\ (x_1,y_1)=(1,-2);(x_2,y_2)=(4,-14) \\ m=(-14-(-2))/(4-1)=(-14+2)/(3)=(-12)/(3) \\ m=-4 \end{gathered}`

We proceed to use the point-slope equation to derive this function:

`\begin{gathered} y-y_1=m(x-x_1) \\ m=-4 \\ (x_1,y_1)=(1,-2) \\ y-(-2)=-4(x-1) \\ y+2=-4x+4 \\ y=-4x+4-2 \\ y=-4x+2 \\ \\ \therefore y=-4x+2 \end{gathered}`