Graph the inequality.
y greater than one eighth x
begin by replacing the inequality symbol with an equal sign and then graphing the corresponding linear equation.
y
greater than
one eighth x
y
equals
one eighth x
replace the inequality symbol by equals.
notice that the equation is in slope-intercept form, y equals mx plus b, where m is the slope and b is the y-intercept. in this case, the slope, m, is one eighth
. the y-intercept, b, is 0.
since the y-intercept is 0, the line passes through the point left parenthesis 0 comma 0 right parenthesis.
using the equation for the line, find a second point on the line. find the value of y when x equals 8.
yequalsone eighth left parenthesis 8 right parenthesis
equals1
draw the line using the slope, y-intercept, and the point left parenthesis 8 comma 1 right parenthesis. a solid line should be drawn if the original inequality contains a less than or equals or greater than or equals symbol. a dashed line should be drawn if the original inequality contains a less than or greater than symbol.
the inequality symbol in y greater than one eighth x
is greater than . the line should be dashed.
the dashed line has a slope of one eighth
and passes through the points left parenthesis 0 comma 0 right parenthesis, and left parenthesis 8 comma 1 right parenthesis . the graph of the line is shown on the right.
inequalities in the form ygreater thanmxplusb or y less than mx plus b can be graphed without using test points. the inequality symbol indicates which half-plane to shade. if y greater than mx plus b comma shade the half-plane above the line y equals mx plus b. if y less than mx plus b comma shade the half-plane below the line y equals mx plus b.
in this case, the half-plane above the line should be shaded. the graph of the inequality y greater than one eighth x
is shown to the right.