If you know a point on a line and the slope of that line, you can determine other points on the line.

 

Example 2

The point (−2,−3) lies on a line with a slope of . Determine four other points on the line. Use the points to graph the line.

Begin by plotting the point.

A line with a slope of has a rise of 4 for every run of 3. Count off this rise and run to determine another point on the line.

 Make sure when you use the method shown that you check the scales on the «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math»-axis and «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«/math»-axis. If the scales aren't the same, the number of units each grid square represents will not be the same going up as going to the right.

Consider plotting a line with a slope of «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»6«/mn»«mn»5«/mn»«/mfrac»«/math» that contains the point (–5, 10) on the grid shown below:

Even though we have only gone up 3 grid squares to each the next point, we have gone up the 6 units specified by the slop because each line on the «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«/math»-axis represents 2 units.

Continue this process to determine other points.

Draw a line through the points.