First, the slopes of the perpendicular lines satisfy the following equation
[tex]\begin{gathered} m_1=\frac{-1}{m_2} \\ \text{ Where}m_1\text{ is the slope of line 1 and} \\ m_2\text{ is the slope of line 2} \end{gathered}[/tex]
In this case, the slope of line 2 is -4 because the equation of the given line is in its point-slope form, that is
[tex]\begin{gathered} y=mx+b \\ \text{ Where m is the slope of the line and} \\ b\text{ is the y-intercept} \end{gathered}[/tex]
Now, using the point-slope formula you can find the equation of line 1
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1)\text{ is a point through which the line passes} \end{gathered}[/tex]
So, you have
[tex]\begin{gathered} m_1=\frac{-1}{m_2} \\ m_2=-4 \\ m_1=\frac{-1}{-4} \\ m_1=\frac{1}{4} \end{gathered}[/tex]
And then
[tex]\begin{gathered} (x_1,y_1)=(-2,7) \\ y-y_1=\frac{1}{4}(x-x_1) \\ y-7_{}=\frac{1}{4}(x-(-2)) \\ y-7_{}=\frac{1}{4}(x+2) \end{gathered}[/tex]
Therefore, the correct answer is A.
[tex]y-7_{}=\frac{1}{4}(x+2)[/tex]
