91Ó°ÊÓ

When determining the slope of a line, you're essentially measuring its steepness. Mathematically, the slope is represented by the letter "m" and can be calculated by using the formula:\[m = \frac{y_2 - y_1}{x_2 - x_1}\]This formula tells us the rate of change between the y-coordinates and the x-coordinates of two points. - If the slope is positive, the line inclines upwards from left to right. - A negative slope means the line descends.- A zero slope indicates a perfectly horizontal line.- An undefined slope suggests a vertical line, where division by zero occurs during the calculation.In our exercise, substituting in the values from the points (-8, 0) and (6, 0), we calculate the slope as zero, illustrating that our line is horizontal, running parallel to the x-axis.

The equation of a line provides a formula we can use to plot every point on that line. There are different forms of linear equations, but for lines with a slope, the **point-slope form** is especially helpful:\[y - y_1 = m (x - x_1)\]Our slope "m" has been determined to be zero in the previous calculation, which simplifies the equation significantly. For a horizontal line, this means the y-value remains constant throughout. Therefore, the equation simplifies to:\[y = b\]In our example, the horizontal line is represented by the equation \( y = 0 \), meaning that for any x-value, the y-coordinate will always be zero. Thus, all points on this line are located along the x-axis.

Understanding coordinates of points is vital for plotting and understanding graphs in a 2D space. Each point is defined by an ordered pair, \((x, y)\), which precisely locates the position on graph paper.- The first number, \(x\), indicates the position relative to the horizontal x-axis.- The second number, \(y\), specifies the position relative to the vertical y-axis.In our specific exercise, we have two points: \((-8, 0)\) and \((6, 0)\). Both these points share the same y-coordinate, which is 0, indicating that these points lie directly on the x-axis. Through understanding these coordinates, we can tell that such points represent a line that doesn't rise or fall, hence confirming a slope of zero, which results in a horizontal line.