The equation of a line is expressed as
y = mx + c
where
m = slope
c = y intercept
Considering the graph as that of an equation instead of an inequality,
slope = (y2 - y1)/(x2 - x1)
slope = (0 - - 1)/(5 - 2) = 1/3
To find c, substitute m = 1/3, x = 5, y = 0 into y = mx + c. We have
0 = 1/3 * 5 + c
0 = 5/3 + c
c = 0 - 5/3 = - 5/3
The equation of the line would be
y = x/3 - 5/3
Rearranging the equation, we have
3y = x - 5
x - 3y = 5
Since the line is broken, it would be less than or greater than.
We would test a point on the shaded part to choose the correct inequality. Taking x = 0 and y = 0, we have
0 - 3 * 0 = 5
0 - 0 = 5
We know that 0 is less than 5
Thus, the correct inequality is
x - 3y < 5