Question

1. the current through a \\(1.6\\ \omega\\) resistor is given by \\(i = \frac{v}{1.6}\\), where \\(v\\) is the voltage in volts and \\(i\\) is in amps.

(a) create a table of \\(i\\)-values when \\(v\\) is \\(0, 2, 4, 6, 8\\), and \\(10\\).
(b) graph this linear equation.
(c) what is the slope of this line?
(d) what is the \\(y\\)-intercept?

Explanation:

Calculate current values

Using the Algebraic Substitution and Table of Values knowledge points

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Plot the linear equation

Using the Graphing Linear Equations knowledge point

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Determine the slope

Using the Slope Formula knowledge point

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Find the y-intercept

Using the y-intercept knowledge point

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Answer:

(a) The table of values for \(V\) and \(I\):

\(V\) (volts)	\(I\) (amps)
2	1.25
4	2.5
6	3.75
8	5
10	6.25

(b) The graph of the linear equation \(I = \frac{V}{1.6}\) is plotted below.

(c) The slope of the line is \(\frac{1}{1.6} = 0.625\).

(d) The \(y\)-intercept (or \(I\)-intercept) is \(0\) (or the point \((0, 0)\)).