On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 1) and (3, 0). Everything above and to the left of the line is shaded.
Which linear inequality is represented by the graph?
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Step-by-step explanation:
Equation of the line with (0 ,-1) and (3, 0)
is y - y1 = m (x - x1)
and m = (y2 - y1)/(x2 - x1)
x1 = 0, y1 = - 1, x2 = 3 and y2 = 0
[y - (-1)] = [0-(-1)/3-0] (x - 0)
=> y + 1 = 1/3 x
=> 3y + 3 = x
=> x - 3y - 3 = 0
as area to the left [towards the origin] is
shaded, the linear inequality is
=> x - 3y - 3 ≤ 0
[to check we put x = 0 and y = 0 then the inequality becomes -3 ≤ 0 which is true which implies the area above and to the left of the line is shaded]
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