Question

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 graph Ordered pairs are $(0,-2),(2,0)$

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

Here ${\mathrm{x}}_1=0,{\mathrm{x}}_2=2$ and ${\mathrm{y}}_1=-2,{\mathrm{y}}_2=0$

$$\begin{gathered} \therefore \mathrm{m}=\frac{0-(-2)}{2-0} \\ =\frac{2}{2} \\ =1 \end{gathered}$$

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

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

$\Rightarrow \mathrm{y}=1\mathrm{x}+\mathrm{c}$ $\because \mathrm{m}=1$

$\Rightarrow -2=1\times 0+\mathrm{c}$ (Putting $\mathrm{y}=-2$ and $\mathrm{x}=0$ i.e., $(0,-2)$)

$$\begin{gathered} \Rightarrow -2=0+c \\ \Rightarrow -2=c \\ \Rightarrow c=-2 \end{gathered}$$

Now again put $c=-2$ in linear function,

$\Rightarrow \mathrm{y}=\mathrm{x}-2$

Hence, Linear function would be $\mathrm{y}=\mathrm{x}-2$.