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?

1. the inductive reactance of a 0.75 h coil is given by \\(x_l = 4.712f\\), where \\(f\\) is the frequency in hertz and \\(x_l\\) is in ohms.

(a) what is the slope of this line?
(b) what is the \\(y\\)-intercept?

1. an electronics store purchased a panel truck for $29,625. they figure that the truck will require an average of $19.65 per day in maintenance and operating costs. the total cost of owning this truck on any given day, \\(t\\), can be represented by a straight line.

(a) what is the slope of this line?

Explanation:

Create a table of values for the current equation

Using the Table of Values knowledge point
For the equation \(I = \frac{V}{1.6}\), we calculate \(I\) for \(V = 0, 2, 4, 6, 8, 10\):

• For \(V = 0\): \(I = \frac{0}{1.6} = 0\)
• For \(V = 2\): \(I = \frac{2}{1.6} = 1.25\)
• For \(V = 4\): \(I = \frac{4}{1.6} = 2.5\)
• For \(V = 6\): \(I = \frac{6}{1.6} = 3.75\)
• For \(V = 8\): \(I = \frac{8}{1.6} = 5\)
• For \(V = 10\): \(I = \frac{10}{1.6} = 6.25\)

Graph the linear equation and find its slope and intercept

Using the Graphing Linear Equations, Slope Formula, and y-intercept knowledge points

• The equation \(I = \frac{1}{1.6}V\) is in slope-intercept form \(y = mx + b\), where the independent variable is \(V\) and the dependent variable is \(I\).
• The slope \(m\) is \(\frac{1}{1.6} = 0.625\).
• The \(y\)-intercept (or \(I\)-intercept) is \(0\), representing the point \((0, 0)\).

Analyze the inductive reactance equation

Using the Inductive Reactance Modeling, Slope Formula, and y-intercept knowledge points
For the linear equation \(X_L = 4.712f\):

• The independent variable is \(f\) and the dependent variable is \(X_L\).
• Comparing \(X_L = 4.712f + 0\) to \(y = mx + b\):
• The slope \(m\) is \(4.712\).
• The \(y\)-intercept (or \(X_L\)-intercept) is \(0\), representing the point \((0, 0)\).

Analyze the total cost function

Using the Cost Function Modeling, Slope Formula, and y-intercept knowledge points
Let \(C\) be the total cost of owning the truck and \(t\) be the number of days.

• The initial purchase cost is a fixed cost of \(\$29,625\).
• The daily maintenance and operating cost is a variable cost of \(\$19.65\) per day.
• The linear equation modeling this is:

$$C = 19.65t + 29625$$

• Comparing this to \(y = mx + b\):
• The slope \(m\) is \(19.65\).

Answer:

Question 3

(a) The table of values for \(I = \frac{V}{1.6}\):

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

(b) The graph of the line \(I = 0.625V\) passes through the points calculated in the table, starting at the origin \((0,0)\).

(c) The slope of this line is \(0.625\) (or \(\frac{5}{8}\)).

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

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Question 4

(a) The slope of this line is \(4.712\).

(b) The \(y\)-intercept (or \(X_L\)-intercept) is \(0\).

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Question 5

(a) The slope of this line is \(19.65\).