Given:
The two points given are,
[tex](-3,2),(-1,6)[/tex]
Required:
The equation of the line passing through given two points.
Explanation:
Let the given two points be
[tex]\begin{gathered} (x_1,y_1)=(-3,2) \\ (x_2,y_2)=(-1,6) \end{gathered}[/tex]
Therefore, by two-point form, the equation of the line passing through two points is given by,
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ \Rightarrow y-2=\frac{6-2}{-1-(-3)}(x-(-3)) \\ \Rightarrow y-2=\frac{4}{2}(x+3) \\ \Rightarrow y-2=2(x+3) \\ \Rightarrow y-2=2x+6 \\ \Rightarrow y=2x+6+2 \\ \Rightarrow y=2x+8 \end{gathered}[/tex]
Final Answer:
The equation of the line passing through given two points is,
[tex]y=2x+8[/tex]
First option is correct.
