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# Using Slopes to Graph Lines

We have graphed a line by making a table of at least two ordered pairs and plotting the ordered pairs on a Cartesian coordinate system.

If we are given only one point on a line, we can graph the line if we also know its slope.

Procedure â€” To Graph a Line Using a Point and the Slope

Step 1 Plot any point on the line.

Step 2 From this point, rise in the y-direction the number of units in the numerator of the slope.

Step 3 Then run in the x-direction the number of units in the denominator of the slope. Plot a point at this location.

Step 4 Draw a line through the two points.

Note:

We â€œriseâ€ in the y-direction and â€œrunâ€ in the x-direction.

positive rise: move up

negative rise: move down

positive run: move right

negative run: move left

Example 1

Graph the line that passes through the point (4, -3) with slope

Solution

Step 1 Plot any point on the line. Plot the given point (4, -3).

Step 2 From this point, rise in the y-direction the number of units in the numerator of the slope.

The slope is We can write this as . Thus, the rise is -2.

From (4, -3), move down 2 units to (4, -5).

Step 3 Then run in the x-direction the number of units in the denominator of the slope. Plot a point at this location.

We wrote the slope as , so the run is 3.

From (4, -5) move 3 units to the right to (7, -5).

Place a dot at (7, -5).

Step 4 Draw a line through the two points. Draw the line through (4, -3) and (7, -5).

Note:

We could also write the slope, , as . Then, the rise is -2 and the run is -3. Using that rise and run, we end up at (1, -1). That point is also on the line.