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The slope of a line is a measure of how steep the line is and the direction it inclines. To find the slope between two points, you can use the slope formula. The slope formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here,

• \( x_1, y_1 \) are the coordinates of the first point
• \( x_2, y_2 \) are the coordinates of the second point

Using this formula, you can substitute in the values for the points to find the slope. Remember, the order of subtracting the points matters! It should be consistent to avoid mistakes. Following this simple rule helps you accurately determine the slope of any line.

Coordinate geometry, or Cartesian geometry, deals with the position of points on a plane using an ordered pair (x, y). Each point's coordinates tell you how far along the x-axis and y-axis the point is located. For instance, in our example, the points are (-1, -2) and (2, 5). Here,

• -1 and 2 are the x-coordinates
• -2 and 5 are the y-coordinates

You plot these points on a graph to visualize the line that passes through them. Coordinate geometry is essential in understanding the precise location of points and how they relate to each other in geometric figures.

Linear equations define a straight line when represented graphically. The standard form of a linear equation is y = mx + b, where:

• m is the slope
• b is the y-intercept

The slope (\(m\)) determines how steep the line is, and the y-intercept (\(b\)) is where the line crosses the y-axis. From our slope calculation, we found \[ m = \frac{7}{3} \] You can also use the points and slope to find the linear equation for the line. If we plug the slope and one of the points into the equation y = mx + b, we can solve for the y-intercept. This linear equation helps you easily graph the line and understand its properties.

Solving for slope step-by-step ensures a clear and accurate solution. Let's revisit the steps: 1. Identify the coordinates: For points (-1, -2) and (2, 5), we label them \( x_1 = -1 \), \( y_1 = -2 \), \( x_2 = 2 \), \( y_2 = 5 \). 2. Recall the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] 3. Plug in the coordinates: \[ m = \frac{5 - (-2)}{2 - (-1)} \] 4. Simplify the numerator: Calculate the difference between the y-coordinates, \[ 5 - (-2) = 5 + 2 = 7 \] 5. Simplify the denominator: Calculate the difference between the x-coordinates, \[ 2 - (-1) = 2 + 1 = 3 \] 6. Find the slope: Combine the simplified numerator and denominator, \[ m = \frac{7}{3} \] Following each step methodically ensures you don't miss out on any calculation detail, providing a robust understanding of the process and accurate answers.