To obtain the answer to this question, we have to derive the equation of the straight line, and thus the following steps are necessary:
Step 1: Recall the formula for the equation of a straight line which passes through two points (x1, y1) and (x2, y2), as shown below:
[tex]y-y_1=(\frac{y_2-y_1}{x_2-x_1})\times(x-x_1)[/tex]
Step 2: Apply the formula to obtain the equation of the straight line, as follows:
[tex]\begin{gathered} \text{Given:} \\ (x_1,y_1)=(-6,4) \\ (x_2,y_2)=(3,1) \\ \text{Thus:} \\ y-y_1=(\frac{y_2-y_1}{x_2-x_1})\times(x-x_1) \\ \Rightarrow y-4_{}=(\frac{1_{}-4}{3_{}-(-6)_{}})\times(x-(-6)) \\ \Rightarrow y-4_{}=(\frac{-3}{3_{}+6_{}})\times(x+6) \\ \Rightarrow y-4_{}=(\frac{-3}{9_{}})\times(x+6) \\ \Rightarrow y-4_{}=-\frac{1}{3}\times(x+6) \end{gathered}[/tex]
Now, imagine we changed our choice of (x1, y1) and (x2, y2), the equation of the straight line becomes:
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