Question

part of the graph representing an electrical signal is shown. the voltage rises steadily from an initial value (a) to a maximum value (b). it then drops instantly to the initial value (c) and repeats such that \\( \overline { a b } \parallel \overline { c d } \\) and \\( \overline { b c } \\) and \\( \overline { d e } \\) are vertical. if \\( a = ( 1,1 ) \\) and \\( b = ( 4,3 ) \\), what is the equation of line cd?

a. \\( - 3 y - 2 x = 5 \\)
b. \\( 3 y - 2 x = 5 \\)
c. \\( 3 y - 2 x = - 5 \\)
d. \\( 3 y + 2 x = 5 \\)

Explanation:

Step1: Calculate the slope of line \(AB\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For points \(A=(1,1)\) and \(B=(4,3)\), we have \(m_{AB}=\frac{3 - 1}{4 - 1}=\frac{2}{3}\). Since \(\overline{AB}\parallel\overline{CD}\), \(m_{CD}=m_{AB}=\frac{2}{3}\).

Step2: Find the coordinates of point \(C\)

Since \(\overline{BC}\) is vertical, the \(x\) - coordinate of \(C\) is the same as that of \(B\). So \(C=(4,1)\) (because the \(y\) - coordinate of \(A\) and \(C\) is the same as the voltage at \(A\) and \(C\) is the initial value).

Step3: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using point \(C=(4,1)\) and \(m = \frac{2}{3}\), we have \(y - 1=\frac{2}{3}(x - 4)\).

Step4: Simplify the equation

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Answer:

C. \(3y - 2x=-5\)