Question

Which of the following equations describes the line shown below? Check allthat apply

Answer 1

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:

`y-y_1=((y_2-y_1)/(x_2-x_1))*(x-x_1)`

Step 2: Apply the formula to obtain the equation of the straight line, as follows:

`\begin{gathered} \text{Given:} \\ (x_1,y_1)=(-6,4) \\ (x_2,y_2)=(3,1) \\ \text{Thus:} \\ y-y_1=((y_2-y_1)/(x_2-x_1))*(x-x_1) \\ \Rightarrow y-4_{}=(\frac{1_{}-4}{3_{}-(-6)_{}})*(x-(-6)) \\ \Rightarrow y-4_{}=(\frac{-3}{3_{}+6_{}})*(x+6) \\ \Rightarrow y-4_{}=(\frac{-3}{9_{}})*(x+6) \\ \Rightarrow y-4_{}=-(1)/(3)*(x+6) \end{gathered}`

Now, imagine we changed our choice of (x1, y1) and (x2, y2), the equation of the straight line becomes: