How do you graph #5x-2y<10#?

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+5)^2-0.125)((x-2)^2+y^2-0.125)(5x-2y-10)=0 [-20, 20, -10, 10]}

We can now graph the inequality. Because there is no "or equal to" clause in the inequality operator we will make the line a dashes line. And, we can shade the left side of the line for the "less than" inequality operator.

graph{5x-2y-10 < 0 [-20, 20, -10, 10]}

To graph the inequality (5x - 2y < 10), follow these steps:

1. First, graph the boundary line (5x - 2y = 10).
2. To graph the boundary line, rearrange the equation to solve for (y): (y = \frac{5}{2}x - 5).
3. Plot the y-intercept at ((0, -5)) and use the slope of (\frac{5}{2}) to find another point, for example, by moving up 5 units and right 2 units from the y-intercept.
4. Draw a dashed line through these points, as the inequality is (<) and not (\leq), indicating that the line is not included in the solution set.
5. Lastly, choose a test point not on the boundary line and substitute its coordinates into the original inequality to determine which side of the line to shade.

That's how you graph the inequality (5x - 2y < 10).