Question

Which choices are equations for the line shown below? Check all that apply.

Answer 1

Step 1:

We will calculate the slope of the line using the formula below

`\begin{gathered} m=(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}`

Bu substituting the values, we will have

`\begin{gathered} m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ m=(2-0)/(2-\left(-2\right)) \\ m=(2)/(2+2) \\ m=(2)/(4) \\ m=0.5 \end{gathered}`

Step 2:

We will represent in the slope-intercept form using the formula below

`\begin{gathered} m=(y-y_1)/(x-x_1) \\ 0.5=(\left(y-0)\right?)/(x-\left(-2\right)) \\ 0.5=(y)/(x+2) \\ y=0.5\left(x+2\right) \\ y=0.5x+1 \end{gathered}`

Step 3:

We will represent the equation in point-slope form using the formula below

`\lparen y-y_1)=m\left(x-x_1\right)`

By substituting the values,we will have

Hence,

The final answers are OPTION B, OPTION C, OPTION D