Question

Use the table to write a linear function that relates $\mathrm{y}$ to $\mathrm{x}$.

Answer 1

Step 1: Find the slope of the line using the points.

From the above table Ordered pairs are $(-8,2),(-4,1),(0,0),(4,-1)$.

We know, slope of the line, $\mathrm{m}=\frac{\mathrm{change}\mathrm{in}\mathrm{y}}{\mathrm{change}\mathrm{in}\mathrm{x}}=\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}$

Now using the two points $(0,0),(4,-1)$, here ${\mathrm{x}}_1=0,{\mathrm{x}}_2=4$ and ${\mathrm{y}}_1=0,{\mathrm{y}}_2=-1$

$$\begin{gathered} \therefore \mathrm{m}=\frac{-1-0}{4-0} \\ =\frac{-1}{4} \\ =-\frac{1}{4} \end{gathered}$$

Step 2: Finding the linear function that relates $\mathrm{y}$ to $\mathrm{x}$.

We know, Linear function: $\mathrm{y}=\mathrm{mx}+\mathrm{c}$

$\Rightarrow \mathrm{y}=-\frac{1}{4}\mathrm{x}+\mathrm{c}$ $\left[\because \mathrm{m}=-\frac{1}{4}\right]$

$\Rightarrow 0=-\frac{1}{4}\times 0+c$ (Putting $\mathrm{y}=0$ and $\mathrm{x}=0$ i.e.,$(0,0)$)

$$\begin{gathered} \Rightarrow 0=0+c \\ \Rightarrow 0=c \\ \Rightarrow c=0 \end{gathered}$$

Now again put $\mathrm{c}=0$ in linear function,

$\mathrm{y}=-\frac{1}{4}\mathrm{x}+0$

Hence, Linear function would be $\mathrm{y}=-\frac{1}{4}\mathrm{x}$.