Combining these two inequalities, we obtain the system of inequalities:
y > 3/4 x - 3/4
y < -1/2 x + 2
To identify the key components and create a system of inequalities for this graph, let's analyze the given information and diagram.
The graph depicts two linear lines, represented by the blue and red lines. The blue line intersects the y-axis at 3, indicating that its y-intercept (b-value) is 3. The slope of the blue line can be determined using the rise/run method. Since the blue line goes from a y-value of 0 to 3 and an x-value of 0 to 4, its slope (m-value) is 3/4.
The red line intersects the y-axis at -2, suggesting that its y-intercept (b-value) is -2. The slope of the red line can be determined similarly, yielding a slope (m-value) of -1/2.
To create a system of inequalities, we need to consider the direction of the lines. Since the blue line slants upwards from left to right, it represents the inequality y > 3/4 x - 3/4. The red line slants downwards from left to right, indicating the inequality y < -1/2 x + 2.
Combining these two inequalities, we obtain the system of inequalities:
y > 3/4 x - 3/4
y < -1/2 x + 2