Question

Which linear inequality is represented by the graph?

y < 3x + 2
y > 3x + 2
y < 1/3x + 2
y > 1/3x + 2​

Answer 1

y > 3x + 2

Explanation:

Find gradient using given points:

m = gradient

Formula:

m = Δy/Δx

m = 9/3 = 3

So, equation of line will be:

y = 3x + a

a is 2 as the point (0, 2) is on the line, 2 units above origin point

The options remaining are:

y > 3x + 2 and y < 3x + 2

Consider any point in the shaded region and compare the y-value of that point with the y-value at the same value of x along the line, e.g. (0, 3) is within the shaded region, the y-value of the line at x = 0 is 2, i.e. the coordinates are (0, 2)

3 > 2 ∴ the correct inequality is y > 3x + 2