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The slope of a line is a measure of its steepness. It shows how much the line rises or falls as you move along it horizontally. If a line goes upwards from left to right, it has a positive slope. If it goes downwards, the slope is negative. To find the slope (\( m \)), we use the formula:

• \[m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\]

Here, \( (x_{1}, y_{1}) \) and \( (x_{2}, y_{2}) \) are the coordinates of two points on the line. Let's look at points \( A(-2, -1) \) and \( B(1, -2) \). By plugging these into the formula, we get:

• \[m = \frac{-2 - (-1)}{1 - (-2)} = -\frac{1}{3}\]

This calculation tells us that for every 3 units of horizontal movement to the right, the line drops by 1 unit. This is why its slope is \(-1/3\).

The Cartesian plane is a two-dimensional space defined by a horizontal axis (x-axis) and a vertical axis (y-axis). Each point on the plane corresponds to a pair of values (x, y), indicating horizontal and vertical distances from the origin \( (0, 0) \). To graph a line, you need at least two points. These points will help determine the line's specific position and direction.In our example, the points are \( A(-2, -1) \) and \( B(1, -2) \). Plot these points:

• Move 2 units to the left and 1 unit down for point A.
• Move 1 unit to the right and 2 units down for point B.

The next step is drawing a line through these plotted points. Because the slope \(-1/3\) is negative, this line will slant downwards from left to right. The line reflects the movement indicated by the slope, connecting point A to point B, and continuing in both directions.

Plotting points is like locating places on a map, where each "address" is a pair of numbers known as coordinates. Each coordinate consists of an \( x \) value (how far left or right) and a \( y \) value (how far up or down).When plotting the point \( A(-2, -1) \):

• The \( x \)-value \(-2\) means moving 2 units to the left of the y-axis.
• The \( y \)-value \(-1\) indicates moving 1 unit below the x-axis.

For the point \( B(1, -2) \):

• The \( x \)-value \(1\) indicates a shift 1 unit to the right of the y-axis.
• The \( y \)-value \(-2\) is 2 units below the x-axis.

By knowing how to plot each point precisely, you can ensure accuracy in graphing lines and understanding geometric concepts.