Respuesta :
If slopes of the given lines are solved and observed, we get the slope of line E is [tex]m_{E}[/tex] = [tex]\frac{-5}{6}[/tex]
As per question statement, the equation for line A is [tex]y = \frac{6x}{5} - 10[/tex] Line A is parallel to line B, which is perpendicular to line C. The line D is perpendicular to line C and perpendicular to line E.
Before solving this question, we need to know about some basic formulas and concepts of equation for a line.
If Lines are parallel, their slopes are equal and if lines are perpendicular, the product of their slopes is -1.
i.e., if [tex]m_{1}[/tex] and [tex]m_{2}[/tex] are slopes of two lines then if,
[tex]m_{1} = m_{2}[/tex] then lines are parallel
Now slope of line A can be found out by formula [tex]y=mx+c[/tex] hence slope of line A [tex]m_{A}[/tex]= [tex]\frac{6}{5}[/tex]
Line B is parallel to A so, [tex]m_{B}[/tex] = [tex]\frac{6}{5}[/tex]
Line C is perpendicular to B so [tex]m_{C} * m_{B} = -1\\m_{C} = \frac{-5}{6}[/tex]
Line D is perpendicular to C so [tex]m_{D} *m_{C} = -1\\m_{D} = \frac{6}{5}[/tex]
Line E is perpendicular to D hence [tex]m_{E} * m_{D} = -1\\m_{E} = \frac{-5}{6}[/tex]
Therefore the slope of line E is [tex]\frac{-5}{6}[/tex]
- Slope of a line: The Slope or Gradient of a straight line shows how steep a straight line is.
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