Summarize this article in one sentence.
You want to find the equation of the line, so to do this you need to isolate the y{\displaystyle y} variable on the left side of the equation using algebra. The right side of the equation should have the x{\displaystyle x} variable, and likely, a constant. For example, for the inequality 3y+9>9x{\displaystyle 3y+9>9x}, you would isolate the y variable by subtracting 9 from both sides, then dividing by 3: 3y+9>9x{\displaystyle 3y+9>9x}3y+99>9x9{\displaystyle 3y+9-9>9x-9}3y>9x9{\displaystyle 3y>9x-9}3y3>9x93{\displaystyle {
rac {3y}{3}}>{
rac {9x-9}{3}}}y>3x3{\displaystyle y>3x-3} To do this, turn the inequality into an equation, and graph as you would any equation of a line. Plot the y-intercept, then use the slope to graph other points on the line. For example, if the inequality is y>3x3{\displaystyle y>3x-3}, you would graph the line y=3x3{\displaystyle y=3x-3}. The y-intercept (the point where the line crosses the y axis) is -3, and the slope is 3, or 31{\displaystyle {
rac {3}{1}}}. So, you would draw a point at (0,3){\displaystyle (0,-3)}. The point above the y-intercept is (1,0){\displaystyle (1,0)}. The point below the y-intercept is (1,6){\displaystyle (-1,-6)}. If the inequality is less than (<{\displaystyle <}) or greater than (>{\displaystyle >}), the line should be dashed, since the solution does not include values equal to the line. If the value is less than or equal to ({\displaystyle \leq }), or greater than or equal to ({\displaystyle \geq }), the line should be solid, since the solution includes values equal to the line. For example, since the inequality is y>3x3{\displaystyle y>3x-3}, the line should be dashed, since the values do not include points on the line. If the inequality shows y>mx+b{\displaystyle y>mx+b} you should shade in the area above the line. If the inequality shows y<mx+b{\displaystyle y<mx+b}, you should shade the area below the line. For example, for the inequality y>3x3{\displaystyle y>3x-3} you would shade above the line.
Solve for y{\displaystyle y}. Graph the line on a coordinate plane. Draw the line. Shade in the appropriate area.