Determining an inequality from a graph requires determining the line that forms the border and including the appropriate inequality sign. The shading of the graph along with the type of line indicates the sign to use.
One way to write the equation of a line is to use the slope-intercept equation, y = mx + b. Slope, represented by "m," is the change in x divided by the change in y. Determine these values by selecting two points on a line and use the grid of the graph to determine the distances. The intercept, represented by "b," is the location where the line crosses the y axis.
Once the values of m and b are determined, substitute them into the equation and change the line to an inequality. If the region under the line is shaded, the "<" symbol is used. If the region above the line is shaded, the ">" symbol is appropriate. A solid line is an indication that points on the line are included in the inequality, and the inequality sign is underlined to add the phrase "or equal to" to the symbol.
If the line is parallel to the x axis, it has a slope of zero, and the equation of the line shows y equal to a constant. If the line is parallel to the y axis, the slope involves division by zero and is undefined, but the equation of the line shows x equal to a constant. Change the line to an inequality by substituting the appropriate inequality symbol.