Question

Use the graph 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 graph Ordered pairs are $(1,3),(2,3),(-1,3),(-2,3)$.

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 $(1,3),(2,3)$, here ${\mathrm{x}}_1=1,{\mathrm{x}}_2=2$ and ${\mathrm{y}}_1=3,{\mathrm{y}}_2=3$

$$\begin{gathered} \therefore \mathrm{m}=\frac{3-3}{2-1} \\ =\frac{0}{1} \\ =0 \end{gathered}$$

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

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

$\Rightarrow \mathrm{y}=\left(0\right)\mathrm{x}+\mathrm{c}$ $\left[\because \mathrm{m}=0\right]$

$\Rightarrow 3=0\times 1+\mathrm{c}$ (Putting $\mathrm{y}=2$ and $\mathrm{x}=0$ i.e.,$(-2,0)$)

$$\begin{gathered} \Rightarrow 3=0+\mathrm{c} \\ \Rightarrow 3=\mathrm{c} \\ \Rightarrow \mathrm{c}=3 \end{gathered}$$

Now again put $\mathrm{c}=3$ in linear function,

$\Rightarrow \mathrm{y}=3$

Hence, Linear function would be $\mathrm{y}=3$.