From the graph above we have a line that has a y-intercept of 6 and an x-intercept of 2. From those points we can find the slope of line and combined with the y-intercept at 6, make an equation in slope-intercept form. We use the points of (0.6) and (2, 0).
m = y₂ - y₁ / x₂ - x₁ = 6 - 0 / 0 - 2 = 6 / -2 = -3
Because the slope is -3 we can write the equation of the line as y = -3x + 6 in slope intercept form. In standard form we add 3x to both sides and write it as 3x + y = 6.
Now we come to the inequality part. The point (0, 0) is not shaded and as such makes the inequality false. Let's see what happens when we put (0,0) into our line.
y = -3x + 6
0 = 0 + 6
0 = 6
Obviously 0 ≠6, but we use y < -3x + 6 the inequality will be true. We want the inequality to be false, so we choose y > -3x + 6. Our line is dashed, so we do not include the "or equal to" in the inequality.
Let's test a true point. Let's try (4, 4)
y > -3x + 6 line in slope intercept form
4 > -3(4) + 6
4 > -12 + 6
4 > -6 TRUE
Thus, y > -3x + 6 is the graph as given.
