contestada

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))

Respuesta :

gmany

Answer:

[tex]\large\boxed{3.\ y-(-7)=-2(x-2)}[/tex]

Step-by-step explanation:

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

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

Let [tex]k:y=m_1x+b_1,\ l:y=m_2x_b_2[/tex].

[tex]l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\if m_1=m_2[/tex]

================================================

We have the equation of the line:

[tex]y=\dfrac{1}{2}x-5\to m_1=\dfrac{1}{2}[/tex]

Therefore

[tex]m_2=-\dfrac{1}{\frac{1}{2}}=-2[/tex]

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

in the point-slope form:

[tex]y-(-7)=-2(x-2)\\\\y+7=-2(x-2)[/tex]

Otras preguntas