Question

Instructions: Match the following graphs with their equation by dragging and dropping from the selection below.

Answer 1

Given

The graphs,

1)

2)

To match the equation which represents the given graphs.

Step-by-step explanation:

1)

Here, consider the points (-4,2) and (-2,-4).

Then, the equation of the straight line is determined by,

`\begin{gathered} (y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1) \\ \Rightarrow(y-2)/(-4-2)=(x-(-4))/(-2-(-4)) \\ \Rightarrow(y-2)/(-6)=(x+4)/(-2+4) \\ \Rightarrow y-2=-(6(x+4))/(2) \\ \Rightarrow y-2=-3(x+4) \end{gathered}`

2)

Here, consider the points (-6,1) and (-5,6).

Then, the equation of the straight line is determined by,

`\begin{gathered} (y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1) \\ \Rightarrow(y-1)/(6-1)=(x-(-6))/(-5-(-6)) \\ \Rightarrow(y-1)/(5)=(x+6)/(-5+6) \\ \Rightarrow y-1=(5(x+6))/(1) \\ \Rightarrow y-1=5(x+6) \end{gathered}`

Hence, the equation of the graph is,

`y-1=5(x+6)`