Learn Before
Graphing the Line Through with Slope
To graph the line passing through the point with slope , apply the four-step point-and-slope procedure.
Step 1 — Plot the given point. Mark on the coordinate plane.
Step 2 — Identify the rise and the run. Because the slope is a whole number, write it as a fraction with denominator :
The rise is and the run is .
Step 3 — Count the rise and the run to mark the second point. Starting at , move up units to reach , then move right unit to reach .
Step 4 — Connect the points with a line. Draw a straight line through and .
Checking with a third point. Since can also be written as , return to and count down units (rise of ) and left unit (run of ) to locate a third point at . If this point falls on the same line, the graph is confirmed correct.
This example illustrates a key technique: when the slope is an integer, express it as a fraction over so that the rise and run can be read directly.
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Elementary Algebra @ OpenStax
Ch.4 Graphs - Elementary Algebra @ OpenStax
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Learn After
A facility manager is mapping a pipe's path on a blueprint grid. The pipe starts at coordinates (-1, -3) and follows a slope of 4. Order the steps below to correctly graph the path of the pipe using the 'rise over run' method.
A landscape architect is designing a straight walkway on a grid map. The walkway begins at the point (-1, -3) and has a slope of 4. When using the 'rise over run' method to plot this walkway, which values represent the vertical change (rise) and the horizontal change (run) from the starting point?
A data analyst is plotting a growth trend on a coordinate grid for a quarterly report. The trend follows a straight line that passes through the historical data point and has a constant slope of 4. Match each graphing component with the correct numerical value used to plot this trend.
A logistics coordinator is mapping a delivery route on a coordinate grid. The route passes through the point (-1, -3) and has a slope of 4. True or False: To correctly identify the 'rise' and 'run' for graphing this route, the whole number slope 4 should be written as the fraction 4/1.
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A facilities manager is verifying a utility line on a blueprint grid. The line passes through the point (-1, -3) and has a slope of 4. To locate a third point for verification, the manager uses the equivalent slope fraction -4/-1, which corresponds to a 'rise' of -4 and a 'run' of ____.
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A manufacturing technician is charting a production efficiency trend on a coordinate grid. The trend follows a straight line passing through the reference point (-1, -3) with a slope of 4. According to the standard verification procedure described in the training manual, what is the coordinate of the third point used to confirm the accuracy of the graphed line?
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