Question

Solve graphically : 5y + 3 ≤ 0

Answer 1

Consider the line whose equation is 5y + 3 ≤ 0, i.e. y = `(-3)/(5)`
This represents a line parallel to X-axis passing through the point `(0, (-3)/5)`.
Draw the line y = `(-3)/(5)`.
To find the solution set, we have to check the position of the origin (0, 0).
When y = 0, 5y + 3 = 5 x 0 + 3 = 3 `cancel<=` 0
∴ the coordinates of the origin does not satisfy the given inequality.
∴ the solution set consists of the line y = `(-3)/(5)` and the non-origin side of the line which is shaded in the graph.