Answered

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RWhich of the following lines is perpendicular to theequation given below?ICUy = -2x + 80 x – 2y = 62x + y = 4O 2x - y = 1x + 2y = 8

RWhich Of The Following Lines Is Perpendicular To Theequation Given BelowICUy 2x 80 X 2y 62x Y 4O 2x Y 1x 2y 8 class=

Sagot :

For two perpendicular lines, the product of the slopes equal -1, such that

[tex]m_1\times m_2=-1[/tex]

The main line's equation is given by

[tex]y=-2x+8[/tex]

On comparing with the slope-intercept form of the equation of a line,

[tex]y=mx+c[/tex]

The slope is given as -2.

Hence, the slope of the second line will be

[tex]\begin{gathered} -2\times m_2=-1 \\ m_2=\frac{-1}{-2} \\ m_2=\frac{1}{2} \end{gathered}[/tex]

Next, we check the options to find which has a slope equal to 1/2.

OPTION 1: x - 2y = 6

Rewriting in the slope-intercept form, we have

[tex]\begin{gathered} -2y=-x+6 \\ \text{Dividing through by -2, we have} \\ y=\frac{1}{2}x-3 \end{gathered}[/tex]

Therefore, the slope of the line is 1/2.

Hence, the FIRST OPTION is correct.

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