Question

Through: (-4, 2), perpendicular. y=4x+1

Answer 1

Two lines are perpendicular when the multiplication of their slopes is equal to minus one. In the line:

`y=4x+1`

the slope is m1 = 4. Therefore, the slope, m2, of a line perpendicular to this one is:

`\begin{gathered} m_1\cdot m_2=-1 \\ 4\cdot m_2=-1 \\ m_2=-(1)/(4) \end{gathered}`

Equation of a line in point-slope form

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

where m is the slope and (x1, y1) is a point on the line.

Substituting with m = -1/4 and the point (-4, 2), we get:

`\begin{gathered} y-2=-(1)/(4)(x-(-4)) \\ y-2=-(1)/(4)(x+4) \end{gathered}`