Question

What is the answer to this question ? Please answer !!

Answer 1

$\text{Let}\ k:y=m_1x+b_1\ \text{and}\ k:y=m_2x+b_2,\ \text{then}\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\-------------------------\\\text{We have}\ 5x-y=-4.\ \text{Convert it to the slope-intercept form:}\\\\5x-y=-4\qquad\text{subtract 5x from both sides}\\\\-y=-5x-4\qquad\text{change the signs}\\\\y=5x+4\to m_1=5\to m_2=-\dfrac{1}{5}\\\\\text{Therefore we have}\ y=-\dfrac{1}{5}x+b.\\\\\text{The line passing through the point (-2, 2).}\\\text{Put the coordinates of the point to the equation:}$

$2=-\dfrac{1}{5}(-2)+b\\\\2=\dfrac{2}{5}+b\qquad\text{subtract}\ \dfrac{2}{5}\ \text{from both sides}\\\\1\dfrac{3}{5}=b\to b=\dfrac{8}{5}\\\\\text{Therefore we have the equation of a line in slope-intercept form:}\\\\y=-\dfrac{1}{5}x+\dfrac{8}{5}\\\\\text{Convert it to the standard form}\ Ax+By=C:\\\\y=-\dfrac{1}{5}x+\dfrac{8}{5}\qquad\text{multiply both sides by 5}\\\\5y=-x+8\qquad\text{add x to both sides}\\\\\boxed{x+5y=8}\to\boxed{[B]}$