Question

What is the equation for the following graph?option 1: y=1/2x+2option 2: y= -1/2x+2option 3: y=2x+2option 4: y= -2x+2

Answer 1

The Solution.

The equation of the given graph is an equation of a line, which is given as the formula below:

`\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where m = slope} \end{gathered}`

First, we shall pick any 2 coordinates in the given line graph:

(-4,0) and (0,2)

`\begin{gathered} (-4,0)\rightarrow(x_1=-4,y_1=0) \\ (0,2)\rightarrow(x_2=0,\text{ }y_2=2) \end{gathered}`

The slope ( m) is given as below:

`m=(y_2-y_1)/(x_2-x_1)`

Substituting the appropriate values given above, we get

`m=(2-0)/(0--4)=(2)/(4)=(1)/(2)`

So, the equation of the graph is :

`\begin{gathered} y-0=(1)/(2)(x--4) \\ \\ y=(1)/(2)(x+4) \\ or \\ 2y=x+4 \end{gathered}`