On graph there is a dotted line and solid line they join at (0,4) then goes down in a shaded downward v shape with points on dotted line (2,0), (5,-6),(7,-10) on solid line (-2,0), (-3,-2),(-4,-4),(-5,-6),(-6,-8),(-7,-10)

Question

Which shows the solution to the system of inequalities
y<-2x+4 and y<2x+4
y < 2x + 4 and y <= 2x + 4
y > -2x + 4 and y <= 2x + 4
y <= 2x + 4 and y <= 2x + 4

Answer 1

To determine the correct system of inequalities represented by the described graph, let's analyze the given information step by step.

1. Lines and Their Equations:

   • The solid line joining points (-2,0), (-3,-2), (-4,-4), (-5,-6), (-6,-8), (-7,-10) suggests the equation is \( y = -2x + 4 \) (since this is a line with a negative slope).
   • The dotted line joining points (2,0), (5,-6), (7,-10) suggests the equation is \( y = 2x - 4 \) (this line has a positive slope).

2. Direction of Inequalities:

   • The solid line indicates a "less than or equal to" (≤) relationship, while the dotted line suggests a "less than" (<) relationship since it represents a region that does not include the line.

3. Shaded Region:

   • The downward V-shape implies you are looking for values of \( y \) that fall below both of these lines.

4. Inequalities: Based on the identified equations of the lines and the descriptions:

   • The solid line \( y \leq -2x + 4 \).
   • The dotted line \( y < 2x - 4 \).

5. Identifying the Correct Set of Inequalities:

   • Considering the analysis, the shaded area below the solid line (y-values are less than or equal to) and below the dotted line (y-values are less than) conforms to the potential inequalities:
     • y < -2x + 4 (for the region below the solid line)
     • y < 2x - 4 (for the region below the dotted line)

Given these observations, we are specifically looking for an inequality that opens downward (reflecting y-values below each of the respective lines).

Conclusion:

The viable option that accurately reflects the scenario described, with the consideration of points and shading indicating less than or equal to and less than, is:

• y < -2x + 4 and y <= 2x + 4.

However, the closest matching sets from your options looks to be: y > -2x + 4 and y <= 2x + 4, as they seem most relevant given your description of the shaded area, assuming "less than" or "greater than" may have been mistyped in your statement. But based on your original input, one can conclude "y <" is vital for a solid indication of the provided graph scenario.

If any additional details are necessary, please provide them so that we can ensure an accurate analysis.