Option C) [tex]y=2x+10[/tex] is correct
Equation of a line passing through points [tex]\boldsymbol{\left ( x_1,y_1 \right ),\left ( x_2,y_2 \right )}[/tex] is given by [tex]\boldsymbol{y-y_1=\left ( \frac{y_2-y_1}{x_2-x_1} \right )\left ( x-x_1 \right )}[/tex]
Given points are as follows:
[tex]\left ( x_1,y_1 \right )=\left ( -7,-4 \right )\\\left ( x_2,y_2 \right )=\left ( -6,-2 \right )[/tex]
Equation of a line is [tex]y+4=\left ( \frac{-2+4}{-6+7} \right )\left (x+7\right )[/tex]
[tex]y+4=2\left ( x+7 \right )[/tex]
[tex]y+4=2x+14[/tex]
[tex]\boldsymbol{y=2x+10}[/tex]
So, option C) is correct.
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