Question

XOSelect the correct answer.Rosa is working on the electrical wiring for a community theater. She creates a diagram of the conduits joining different areas of thetheater on a coordinate grid and uses the line y=-4x+3 to represent the conduit between the stage and the dressing room. Thecondult between the ticket window and the security office passes through the point (4,7) on the grid and is perpendicular to the condultbetween the stage and dressing room.What is the equation of the line representing the conduit between the ticket window and the security office?

Answer 1

The product of the slopes of the perpendicular lines is -1

That means if the slope of one of them is m, then the slope of the other is -1/m

(we reciprocal it and change its sign)

The given equation is

$y=-4x+3$

The slope of the line of the equation y = mx + b is m

Then the slope of the given line is -4

To find the slope of the perpendicular line to it, reciprocal it and change its sign

Then the slope of the perpendicular line is

$m_P=\frac{1}{4}$

Substitute it in the form of the equation

$y=\frac{1}{4}x+b$

To find b we will use the given point (4, 7) which lies on the perpendicular line

Substitute x by 4 and y by 7 in the equation

$\begin{gathered} 7=\frac{1}{4}(4)+b \\ 7=1+b \\ 7-1=1-1+b \\ 6=b \end{gathered}$

Substitute the value of b in the equation

$y=\frac{1}{4}x+6$

The answer is y = 1/4x + 6

$y=\frac{1}{4}x+6$

The answer is the last choice