Answer:
Step 1:
We will calculate the slope of the line using the formula below
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \left(x_1,y_1\right)\Rightarrow\left(-2,0\right) \\ \lparen x_2,y_2)\Rightarrow\left(2,2\right) \end{gathered}[/tex]Bu substituting the values, we will have
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{2-0}{2-\left(-2\right)} \\ m=\frac{2}{2+2} \\ m=\frac{2}{4} \\ m=0.5 \end{gathered}[/tex]Step 2:
We will represent in the slope-intercept form using the formula below
[tex]\begin{gathered} m=\frac{y-y_1}{x-x_1} \\ 0.5=\frac{\left(y-0)\right?}{x-\left(-2\right)} \\ 0.5=\frac{y}{x+2} \\ y=0.5\left(x+2\right) \\ y=0.5x+1 \end{gathered}[/tex]Step 3:
We will represent the equation in point-slope form using the formula below
[tex]\lparen y-y_1)=m\left(x-x_1\right)[/tex]By substituting the values,we will have
[tex]\begin{gathered} \operatorname{\lparen}y-y_1)=m\left(x-x_1\right) \\ y-0=0.5\left(x-\left(-2\right)\right) \\ y-0=0.5\left(x+2\right) \\ \\ \operatorname{\lparen}y-y_2)=m\lparen x-x_2) \\ y-2=0.5\left(x-2\right) \end{gathered}[/tex]Hence,
The final answers are OPTION B, OPTION C, OPTION D
