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.

Explanation:

1)

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

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

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

2)

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

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

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

Hence, the equation of the graph is,

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