Questions: Which set of inequalities represents the solution to the system of inequalities shown in the graph? y<3x+2 and 2y≥6x-4 y≤3x+2 and 2y>6x-4 y≥3x+2 and 2y>6x-4 y<3x+2 and 2y≤6x-4

Which set of inequalities represents the solution to the system of inequalities shown in the graph?
y<3x+2 and 2y≥6x-4
y≤3x+2 and 2y>6x-4
y≥3x+2 and 2y>6x-4
y<3x+2 and 2y≤6x-4

Transcript text: Which set of inequalities represents the solution to the system of inequalities shown in the graph? $y<3 x+2$ and $2 y \geq$ $6 x-4$ $y \leq 3 x+2$ and $2 y>$ $6 x-4$ $y \geq 3 x+2$ and $2 y>$ $6 x-4$ $y<3 x+2$ and $2 y \leq$ $6 x-4$

Solution

Solution Steps

Step 1: Identify the equations of the lines

From the graph, we can see two lines. We need to determine their equations. The lines appear to be in the slope-intercept form $ y = mx + b $.

Step 2: Determine the slope and y-intercept of each line

The first line has a positive slope and intersects the y-axis at $ y = 2 $. The equation is $ y = 3x + 2 $.
The second line has a negative slope and intersects the y-axis at $ y = -4 $. The equation is $ y = -3x - 4 $.

Step 3: Determine the inequality signs

For the first line $ y = 3x + 2 $, the shaded region is above the line, indicating $ y \geq 3x + 2 $.
For the second line $ y = -3x - 4 $, the shaded region is below the line, indicating $ y \leq -3x - 4 $.