To make that graph you follow these steps.
1) Set the cartesian coordinate system:
- vertical axis: y
- horizontal axis: x
- positive x-semi axis: to the right
- negative x-semi axis: to the left
- positive y-semi axis: upward
- negative y semi axis: dwonward
2) solve the inequality for y:
given: -2x + 5y > 15
transpose-2x: 5y > 15 + 2x
divide by 5: y > 3 + (2/5)x
3) Graph
- draw the line y = 3 + (2/5)x, using a dotted line (i.e. - - - - - -)
- remember that 3 is the y intercept, and 2/5 is the slope
- the line is dotted because the solution does not include the points in the line.
- the solution is the region above and to the left of the dotted line.
4) See the figure attached for better visualization: the pink region is the solution of the inequality.