Question

Which equation represents a line that is perpendicular to the line passing through (-4,7) and (1,3)?A. y =x + 8B.y =-x + 6C.y =x - 3D. y = -x - 2

Answer 1

If two lines of slopes m1 and m2 are perpendicular, then:

`m_1\cdot m_2=-1`

The slope of a line passing through points (x1, y1) and (x2, y2) is:

`\begin{equation*} m=(y_2-y_1)/(x_2-x_1) \end{equation*}`

We are given the points of the first line (-4, 7) and (1, 3). Calculate the slope

`m_1=(3-7)/(1+4)=-(4)/(5)`

The slope of the perpendicular line is:

`m_2=-(1)/(m_1)=-(1)/(-(4)/(5))=(5)/(4)`

The equation of the perpendicular line has the form:

`y=(5)/(4)x+b`

None of the options has the correct answer.