How do you graph #2x-3y<6# on the coordinate plane?

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

graph{(x^2+(y+2)^2-0.035)((x-3)^2+y^2-0.035)(2x-3y-6)=0 [-10, 10, -5, 5]}

Now, we can shade the left side of the line.

The boundary line will be changed to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(2x-3y-6) < 0 [-10, 10, -5, 5]}

To graph the inequality 2x - 3y < 6 on the coordinate plane, follow these steps:

1. First, rewrite the inequality in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
2. Solve the inequality for y to isolate it on one side.
3. Then, plot the y-intercept (0, b) on the y-axis.
4. Use the slope to find another point on the line. The slope represents the change in y for every unit change in x.
5. Draw a dashed line through the two points. Since the inequality is strictly less than (<), the line should be dashed to indicate that the points on the line are not included in the solution set.
6. Finally, choose a test point not on the line and substitute its coordinates into the original inequality to determine which side of the line to shade.

Following these steps will allow you to accurately graph the inequality 2x - 3y < 6 on the coordinate plane.