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What is the slope of a line perpendicular to the line whose equation is2x + 10y = 20. Fully simplify your answer.

Sagot :

For two lines to be perpendicular, if you multiply their slopes, the answer should be -1.

The first thing we need to do is to find the slope of this equation. Given that the equation of the slope is y=mx + b and m = slope,

[tex]2x+10y=20[/tex][tex]10y=-2x+20[/tex][tex]\frac{10y}{10}=\frac{-2x+20}{10}[/tex][tex]y=-\frac{1}{5}+2[/tex]

Given this equation, we now have a slope of -1/5.

Since we need the product of two slopes to be -1, we divide -1 by -1/5.

[tex]m_1=-\frac{1}{5};m_2=?[/tex][tex]m_1m_2=-1[/tex][tex]-\frac{1}{5}m_2=-1[/tex][tex]\frac{-\frac{1}{5}m_2}{-\frac{1}{5}}=\frac{-1}{-\frac{1}{5}}[/tex][tex]m_2=5[/tex]

Therefore, in order for an equation to be perpendicular to 2x + 10y = 20, it must have a slope of 5.

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