Question

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

Answer 1

Step 1: Finding the slope of line from the graph.

From the graph we have points $(0,-2)$ $(1,2),(-2,6)$ and $(1,-6)$.

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 two points $(0,-2)$ and $(1,2)$

Here, ${\mathrm{x}}_1=0,{\mathrm{x}}_2=1$ and ${\mathrm{y}}_1=-2,{\mathrm{y}}_2=2$

Now putting the values we get,

$$\begin{gathered} \mathrm{m}=\frac{2-(-2)}{1-0} \\ =\frac{2+2}{1} \\ =4 \end{gathered}$$

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

We know, linear equation of a line is $\mathrm{y}=\mathrm{mx}+\mathrm{c}$

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

$\Rightarrow -2=4\times \left(0\right)+\mathrm{c}$ (Putting $\mathrm{y}=-2$ and $\mathrm{x}=0$ i.e., $(0,-2)$)

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

Now again put $\mathrm{c}=-2$ in linear equation,

$\Rightarrow \mathrm{y}=4\mathrm{x}-2$

Hence, linear function is $\mathrm{y}=4\mathrm{x}+2$.