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Sagot :
First of all we are going to find the slope perpendicular to the equation y = -1/2 x +6.
We need to remember that two slopes are perpendicular if its product is equal to -1. Like this:
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ m_1=-\frac{1}{2}_{} \\ m_2=-\frac{1}{m_1}=-\frac{1}{-\frac{1}{2}}=2 \\ m_2=2 \end{gathered}[/tex]Now, we find the equation of the line using the general form:
[tex](y-y_1)=m(x-x_1);\text{ }[/tex]m - slope
[tex](x_1,y1)=(-4,2)_{}[/tex]That was a point of the line, now:
[tex]\begin{gathered} (y-2)=2(x-(-4)) \\ y-2=2x+8 \\ y=2x+10 \end{gathered}[/tex]Finally, the equation of the line that passes through (-4,2) and is perpendicular to the equation y = -1/2x+6 is
y=2x+10
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