Question

Identify an equation in point-slope form for the line perpendicular to y=-4x - 1 that passes through (-2, 7). A. y-7 - 4(x+2) B.7 = -4(x + 2) C. yu? -(-2 Dy+2=(x-7)

Answer 1

First, the slopes of the perpendicular lines satisfy the following equation

`\begin{gathered} m_1=(-1)/(m_2) \\ \text{ Where}m_1\text{ is the slope of line 1 and} \\ m_2\text{ is the slope of line 2} \end{gathered}`

In this case, the slope of line 2 is -4 because the equation of the given line is in its point-slope form, that is

`\begin{gathered} y=mx+b \\ \text{ Where m is the slope of the line and} \\ b\text{ is the y-intercept} \end{gathered}`

Now, using the point-slope formula you can find the equation of line 1

`\begin{gathered} y-y_1=m(x-x_1) \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1)\text{ is a point through which the line passes} \end{gathered}`

So, you have

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

And then

`\begin{gathered} (x_1,y_1)=(-2,7) \\ y-y_1=(1)/(4)(x-x_1) \\ y-7_{}=(1)/(4)(x-(-2)) \\ y-7_{}=(1)/(4)(x+2) \end{gathered}`

Therefore, the correct answer is A.

`y-7_{}=(1)/(4)(x+2)`