Learn Before
Finding the Slope from a Graph
A line is graphed on the -coordinate plane passing through the points and . To find its slope, apply the four-step rise-over-run procedure.
Step 1 — Locate two points with integer coordinates. The points and both have integer coordinates, so mark them on the graph.
Step 2 — Sketch a right triangle. Starting at the left point , draw a vertical leg upward to and then a horizontal leg to the right to reach . The line from to forms the hypotenuse of this right triangle.
Step 3 — Count the rise and the run. The vertical leg goes from up to , so the rise is . The horizontal leg goes from to , so the run is .
Step 4 — Take the ratio of rise to run:
The slope of the line is , which means increases by units for every units that increases. This example demonstrates the same right-triangle technique used on a geoboard, now applied to a line on the coordinate plane.
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Elementary Algebra @ OpenStax
Ch.4 Graphs - Elementary Algebra @ OpenStax
Algebra
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Prealgebra
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An urban planner is examining a graph of a road elevation change. To find the slope of the road from the graph, place the following steps in the correct order according to the standard procedure for calculating slope from a visual representation.
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A maintenance supervisor is analyzing a graph of a building's energy consumption, which shows a steady decrease over the last week. When following the standard procedure to calculate the slope of this line, how should the supervisor record the 'rise' if the vertical distance between the two selected points is downward?
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Learn After
A project manager is using a coordinate plane to track project milestones. To find the slope of the progress line using the rise-over-run method, arrange the following steps in the correct sequence.
A financial analyst is graphing the quarterly profit growth of a startup on a coordinate plane. The growth line passes through the points (0, -3) and (5, 1). When using the rise-over-run method to calculate the slope of this profit line, what is the value of the 'rise' between these two points?
An infrastructure project manager is graphing the slope of a new communication cable trench on a coordinate plane. The trench path passes through the points (0, -3) and (5, 1). Match each component of the slope calculation to its correct numerical value based on these two points.
A logistics manager is mapping an access road on a coordinate plane. The road follows a line passing through the points (0, -3) and (5, 1). True or False: A slope of 4/5 for this road indicates that the vertical elevation increases by 4 units for every 5 units of horizontal distance.
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A civil engineering intern is documenting the slope of a highway section graphed on a coordinate plane. The section passes through the points (0, -3) and (5, 1). To ensure an accurate count of the rise and run using the standard four-step procedure, the intern must first identify two points on the line that have ____ coordinates.
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A project analyst is graphing the cost efficiency of a new workflow on a coordinate plane. The efficiency line passes through the points (0, -3) and (5, 1). Based on the standard rise-over-run procedure, what is the slope (m) of this line?
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