Question

2) What is the inequality that this graph represents? -15 # 3 6 x​

Answer 1

Answer:  $y < -\frac{1}{2}x+3$

This is the same as writing y < (-1/2)x+3

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Explanation:

The dashed boundary line goes through (0,3) and (4,1)

Apply the slope formula for those two points

m = (y2-y1)/(x2-x1)

m = (1-3)/(4-0)

m = -2/4

m = -1/2

The slope of the dashed line is -1/2. The y intercept is 3. So we go from y = mx+b to y = (-1/2)x+3 to represent the equation of the dashed line. This is the same as writing $y = -\frac{1}{2}x+3$

We shade below the dashed line to represent the inequality $y < -\frac{1}{2}x+3$. Points in the shaded region are solutions to the inequality. One example point is (0,0).

Note that we don't have "or equal to" as part of the inequality sign because we are not including points on the boundary. A solid line, rather than a dashed line, would include points on the boundary.