COORDINATE GRAPHS

FINDING THE SLOPE

Concept: A coordinate graph is a system for finding the location of a point, or several points, on a flat surface called a plane. A coordinate graph is formed from two axis lines that cross at a point called the origin. The horizontal line is the x-axis and the vertical line is the y-axis. Both lines are marked as number lines with the origin at zero. The axes divide the graph into four quadrants, labeled I, II, III, and IV.

Each point on the grid is named by two numbers, an x-coordinate and a y-coordinate. The x-coordinate is always written first; the y-coordinate is always written second. Together the coordinates are called an ordered pair and are enclosed in parentheses, separated by a comma like this: (x, y) .

Slope is a number that measures the steepness of a line. Slope is the ratio of rise to run, where rise is a measurement of vertical distance and run is a measurement of horizontal distance.

Slope can be positive or negative. All lines that rise as they more left to right have a positive slope. All lines that fall as they move left to right have negative slope.

Positive Slope Negative Slope

Steps for Finding the Slope

Step 1 | Imagine a line traversing both points on the graph.
Step 2 | Starting at either point, count the number of units up or down to reach the level of the second point. This is the rise of the line.
Step 3 | From this intermediate point, count the units left or right to reach the second point. This is the run of the line.
Step 4 | Write the slope as a fraction, rise over run. Reduce the fraction to its lowest terms.
Step 5 | Decide whether the slope is positive or negative. All lines that rise as they more left to right have a positive slope. All lines that fall as they move left to right have negative slope.

Example Find the slope of the line traversing the two points in the graph below.

Step 1 | Imagine a line traversing both points on the graph. | See green line in graph
Step 2 | Starting at either point, count the number of units up or down to reach the level of the second point. This is the rise of the line. | Start at Point A and count the number of units up. There are 6 units. The rise is 6.
Step 3 | From this intermediate point, count the units left or right to reach the second point. This is the run of the line. | Count the number of units right until you reach Point B. There are 2 units. The run is 2.
Step 4 | Write the slope as a fraction, rise over run. Reduce the fraction to its lowest terms. |
Step 5 | Decide whether the slope is positive or negative. All lines that rise as they more left to right have a positive slope. All lines that fall as they move left to right have negative slope. | The slope rises as it moves from left to right so it is positive.