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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. The leftmost point is .
Step 2 — Sketch a right triangle. Starting at the left point , draw a vertical leg downward to and then a horizontal leg to the right to reach .
Step 3 — Count the rise and the run. The vertical leg goes from down to , so the rise is (negative because the line moves downward). 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 . This provides another example of a negative slope, where the line drops units for every units it moves to the right.
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Intermediate Algebra @ OpenStax
Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
Algebra
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Learn After
As a data analyst reviewing a project's performance graph, you notice a downward trend line passing through the points and . To formally calculate the rate of this decline, you must apply the geometric rise-over-run procedure. Arrange the following steps in the correct order to find the slope from the graph.
A maintenance technician is tracking a pressure drop in a hydraulic system. The pressure readings are recorded on a graph, and the technician identifies two points on the line: and . To analyze the rate of change, the technician uses the rise-over-run method. Match each geometric component of the slope calculation with its correct numerical value based on these two points.
A telecommunications technician is graphing the elevation change of a fiber optic cable as it is laid underground. The site map shows the cable follows a straight line passing through the coordinates and . What is the slope of this line?
A civil engineer is mapping the grade of a new wastewater line on a site plan. The line passes through the survey points and . True or False: Based on these coordinates, the slope of the line is .
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A field technician is mapping the grade of a drainage pipe on a site plan. The pipe's alignment is represented by a line passing through the points and . To calculate the slope using the rise-over-run method, the technician identifies the vertical change. For this specific line, the numerical value of the rise is ____.