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Solving equations is a fundamental skill in math that helps you find the value of unknown variables. In this exercise, we have the equation \( y = 20x + 60 \). To find solutions, you need to choose values for \( x \) and then calculate the corresponding \( y \) values using those \( x \) values. Here’s how you can do it:

1. Choose three values for \( x \). In the example, we chose \( x = -2 \), \( x = 0 \), and \( x = 2 \).
2. Substitute these \( x \) values into the equation one by one to find the corresponding \( y \) values.
3. For \( x = -2 \), the equation becomes \( y = 20(-2) + 60 \). This simplifies to \( y = -40 + 60 = 20 \).
4. For \( x = 0 \), the equation is \( y = 20(0) + 60 \) which simplifies to \( y = 60 \).
5. For \( x = 2 \), the equation becomes \( y = 20(2) + 60 \) which simplifies to \( y = 100 \).

By plugging in different values of \( x \), you calculate corresponding \( y \) values and find pairs of solutions like \((-2, 20)\), \((0, 60)\), and \((2, 100)\). These pairs represent the points on a graph.

Graphing linear equations helps us visualize the solutions of an equation. Once you've found your points from solving the equation, you can plot them on a graph to see how they align. To graph the equation \( y = 20x + 60 \) follow these easy steps:

1. Take your solution points from the equation-solving step. We have the points \((-2, 20)\), \((0, 60)\), and \((2, 100)\).
2. Plot each point on a coordinate plane. The x-axis represents the value of \( x \) and the y-axis represents the value of \( y \).
3. Place a dot at each point. For instance, put a dot where \( x = -2 \) and \( y = 20 \) intersect.
4. Once all points are plotted, draw a line through these points. This line represents all the possible solutions to the equation \( y = 20x + 60 \).

The line will be straight because it is a linear equation. Linear equations always graph as straight lines.

A coordinate plane is a two-dimensional surface where we can graph points, lines, and curves. It consists of two perpendicular lines called axes. Here's a breakdown:

1. **Axes**: The horizontal line is called the x-axis, and the vertical line is called the y-axis. Together they divide the plane into four quadrants.
2. **Quadrants**: The four regions are labeled as Quadrant I, Quadrant II, Quadrant III, and Quadrant IV, starting from the upper right and moving counterclockwise.
3. **Points**: Each point on the plane can be represented by an ordered pair \((x, y)\), where \( x \) represents the horizontal position and \( y \) represents the vertical position.
4. **Plotting Points**: You can plot points by starting at the origin \((0,0)\) where both axes meet. Move horizontally to the x-value and then vertically to the y-value.

For instance, to plot the point \((-2, 20)\), start at the origin, move left 2 units (since -2 is negative), and then move up 20 units. Place a dot where these two positions meet. The coordinate plane is crucial for visualizing and understanding algebraic concepts like graphing linear equations.