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Slope Line:

One of the most important properties of a straight line is in how it angles away from the horizontal. This concept is reflected in something called the slope of the line. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line. The slope of a vertical line is undefined

This is because any vertical line has a Δx or run of zero. Whenever zero is the denominator of the fraction in this case of the fraction representing the slope of a line, the fraction is undefined. The slope of a horizontal line is zero

This is because any horizontal line has a . ΔY or rise of zero. Therefore, regardless of what the run is the fraction representing slope has a zero in its numerator. Therefore, the slope must evaluate to zero. When the slope of the line is 0, you know that the line is horizontal and you know it's a vertical line when the slope of a line is undefined. y = mx + b is the equation that represents the line and the slope of the line with respect to the x-axis which is given by tan θ = m. This is the slope-intercept form of the equation of a line.

When the slope passes through a point A(x1, y1) then y1 = mx1 + b or with subtraction y - y1 = m (x - x1)

You now have the slope-point form of the equation of a line. A number which is used to indicate the steepness of a line, as well as indicating whether the line is tilted uphill or downhill. Slope is indicated by the letter m.

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