Respuesta :
Given that Line p is represented by the equation;
[tex]2x-y=-5[/tex]Re-writing the equation in the slope intercept form, we have;
[tex]y=2x+5[/tex]Also, line r passes through point (6,4), and is perpendicular to line p;
The slope of line r can be calculated using the formula for perpendicular lines;
[tex]m_p\times m_r=-1[/tex]The product of the slope of two perpendicular lines equals -1.
[tex]\begin{gathered} m_r=\frac{-1}{m_p} \\ m_p=2 \\ m_r==\frac{-1}{2} \end{gathered}[/tex]Finally, since we have the slope of line r, let us apply the point slope equation of a line to get the equation of line r;
[tex]y-y_1=m(x-x_1)[/tex]Given the point;
[tex]\begin{gathered} (x_1,y_1)=(6,4) \\ m_r=\frac{-1}{2} \end{gathered}[/tex]So, subtituting this values, we have;
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