What equation can be used to show that the slope of the line is the same between any two points?
rise 1 · run 1 = rise 2 · run 2
rise 1
—— =
run 1 run 2
rise 1 + run 1 = rise 2 + run 2
run 1
—— =
rise 2
rise 1
What equation can be used to show that the slope of the line is the same between any two points?
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To show that the slope of the line is the same between any two points, you can use the formula for slope:
[
text{slope} = frac{text{rise}}{text{run}} = frac{y_2 – y_1}{x_2 – x_1}
]
This equation states that the slope (m) is the ratio of the change in y (rise) to the change in x (run) between two points ((x_1, y_1)) and ((x_2, y_2)). The slope remains consistent regardless of which two points you select on a linear line because the ratio of vertical change to horizontal change is constant. Thus, the answer can also be expressed as:
[
frac{rise_1}{run_1} = frac{rise_2}{run_2}
]
This ensures that the slope calculated remains the same between any two points on the line. If you want to dive deeper or have further questions, feel free to check the extended services page!