What is the slope of a line that passes through (-14, 13) and (7, 0)?
Solution:
The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. So the change in y coordinate with respect to the change in x coordinate can be written as,
m = Δy/Δx, where,m is the slope
Also, tan θ = Δy/Δx. Hence, we also refer to tan θ to be the slope of the line.
The slope of line joining (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/ (x₂ - x₁)
Here (x₁, y₁) = (-14, 13) and (x₂, y₂) = (7, 0)
∴ Slope = m = (0 - 13)/(7 - (-14)) = -13/21 = -13/21
Note: Slope of the line can also be calculated if the angle(ፀ) made by the line with positive direction of x axis is given using slope = m = tan ፀ
Example: Find the slope of the line containing two points (5, 7) and (-3, 7)
The slope of line joining (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/ (x₂ - x₁)
Here (x₁, y₁) = (5, 7) and (x₂, y₂) = (-3, 7)
∴ Slope = m = -7 - 7/ -3 -5 = 0/-8 = 0
Thus we may note that if the slope of the line is zero then the line is parallel to the x- axis.
What is the slope of a line that passes through (-14, 13) and (7, 0)?
Summary:
The slope of a line that passes through (-14,13) and (7,0) is -13/21
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