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:

$m=\frac{y2-y1}{x2-x1}=\frac{1-3}{0-(-1)}=-\frac{2}{1}=-2$

Using the point-slope equation:

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

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For the 2nd table:

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

Let's find the slope:

$m=\frac{4-6}{0-(-3)}=-\frac{2}{3}$

Using the point-slope equation:

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