Question

Tabitha is trying to find the equation of a line perpendicular to y= 1/2x - 5 in slope-intercept form that passes through the point (2, -7). which of the following equations will she use.

1. y-(-7) = 1/2(x-2)
2.y-2=1/2(x-(-7))
3.y-(-7)=-2(x-2)
4.y-2=-2(x-(-7))

Answer 1

`\large\boxed{3.\ y-(-7)=-2(x-2)}`

Explanation:

The point-slope form of an equation of a line:

`y-y_1=m(x-x_1)`

m - slope

Let
`k:y=m_1x+b_1,\ l:y=m_2x_b_2`.

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We have the equation of the line:

`y=(1)/(2)x-5\to m_1=(1)/(2)`

Therefore

`m_2=-(1)/((1)/(2))=-2`

Put it and coorinates of the point (2, -7) to the equation of a line

in the point-slope form:

`y-(-7)=-2(x-2)\\\\y+7=-2(x-2)`