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The equation of a line is a mathematical way to describe all the points that lie on a specific line in a coordinate plane. The most common form used is the slope-intercept form, expressed as \( y = mx + b \). Here, "\( y \)" is the dependent variable, and "\( x \)" is the independent variable. The expression \( mx \) represents the slope of the line multiplied by the variable \( x \), and \( b \) is the y-intercept.

• **Slope-intercept form:** \( y = mx + b \)
• **Variables:** \( x \) and \( y \)
• **Constants:** \( m \) (slope) and \( b \) (y-intercept)

Using this form, you can quickly determine how steep a line is and where it crosses the y-axis.
To find the equation of a line, you need at least the slope of the line and a point through which it passes. In our exercise, the slope is given as \( m = -5 \), and the line contains the point (-2, -3). These pieces of information help in forming the full equation of the line.

The slope of a line defines its steepness and direction. It is usually represented by the letter "\( m \)" in mathematics. A positive slope means the line is increasing, moving upwards as it goes from left to right, whereas a negative slope indicates a decreasing line, moving downwards. When the slope is zero, the line is horizontal and does not rise or fall.
For the example given in the exercise, the slope is \( m = -5 \). This slope tells us a few important things:

• The line decreases from left to right since the slope is negative.
• For every one unit it moves horizontally (right), it moves down by 5 units vertically.

Understanding the slope allows you to visualize how the line behaves in a graph, giving you insight into its angle and steepness relative to the horizontal axis.

The y-intercept is the point where a line crosses the y-axis. It is represented by "\( b \)" in the slope-intercept form equation \( y = mx + b \). The y-intercept provides a starting point on the graph where \( x \) is zero, making it an essential part of plotting the line.
From the step-by-step solution, we calculated the y-intercept to be \( b = -13 \). Here's how we reached this result:

• We used the point (-2, -3) in the equation \( y = mx + b \).
• We substituted these values into the equation: \[-3 = -5(-2) + b\]
• Solving the equation for \( b \), we find that \( b = -13 \).

This means the line crosses the y-axis at -13, indicating its vertical position in the graph. The y-intercept helps determine the exact line placement on the coordinate plane.