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Graphing linear equations is an essential skill in mathematics. A linear equation represents a straight line when graphed on a coordinate plane. To graph one, you usually need to find at least two points that lie on the line.
For instance, in the provided solutions, we calculated values for function 'a' at different points: \(x = -100, 0, 100\). We found the corresponding \(f(x)\) values: \(0, 10, 20\).
To graph these points, plot them on the coordinate plane and draw a straight line through them. This line represents all possible solutions of the equation \(f(x) = 0.10x + 10\).
This process is similar for function 'b', where the points \((-0.5, 75), (0, 100), (0.5, 125)\) were plotted and connected with a straight line to represent the function \(h(x) = 50x + 100\).

Function tables help organize values of \(x\) and their corresponding function values \((f(x))\). Completing a function table involves substituting \(x\) values into the given function and calculating the result.
For example, in table 'a', we calculated \(f(x)\) values using the function \(f(x) = 0.10x + 10\).

• When \(x = -100\), \(f(-100) = 0\).
• When \(x = 0\), \(f(0) = 10\).
• When \(x = 100\), \(f(100) = 20\).

We then filled in these values to complete the table:

• \begin{array}{|c|c|}\begin{tabular}{|c|c|}x & f(x) = 0.10x + 10 \ \begin{array}{|-100 & 0 \ x & 10 \ 100 & 20 \ \begin{array}{|c|}-100 & 0 \0 & 10 \100 & 20 \ \begin{array}

A coordinate plane is a two-dimensional surface formed by two perpendicular number lines: the x-axis (horizontal) and the y-axis (vertical). Each point on the plane is identified by an ordered pair \((x, y)\).

• The x-axis represents the independent variable.
• The y-axis represents the dependent variable, which is a function of x (typically written as \(f(x)\) or \(h(x)\).

To plot a point, you move horizontally to the x-coordinate and vertically to the y-coordinate. For graphing lines, plot at least two points from your function table and then draw a straight line through them.In this example, the points for function 'a' were \((-100, 0), (0, 10), (100, 20)\), and for function 'b', the points were \((-0.5, 75), (0, 100), (0.5, 125)\). Both lines were graphed on the coordinate plane to visualize the relationships defined by the linear functions.