Solver system of inequalities by graphing why it's greater than or equal to 1/4 x - 3

To solve the inequality y ≥ (1/4)x - 3 by graphing, follow these steps:

Step 1: Graph the line

1. Identify the y-intercept: The y-intercept of the line y = (1/4)x - 3 occurs when x = 0.

   • Plugging in x = 0, we get: \[ y = (1/4)(0) - 3 = -3 \]
   • So, the y-intercept is (0, -3).

2. Identify another point: To find another point on the line, choose a value for x. Let’s use x = 4.

   • Plugging in x = 4: \[ y = (1/4)(4) - 3 = 1 - 3 = -2 \]
   • So, another point on the line is (4, -2).

3. Draw the line: Plot the points (0, -3) and (4, -2) on a graph. Draw a solid line through the points because the inequality includes equal to (≥).

Step 2: Shade the appropriate region

• Since we need to find where y is greater than or equal to (1/4)x - 3, shade the area above the line. This area represents all the points (x, y) that satisfy the inequality.

Graph Summary

• The line should be solid because it's greater than or equal to.
• The region above this line represents all the (x, y) pairs satisfying the inequality y ≥ (1/4)x - 3.

Step 3: Interpretation

• Any point in the shaded area is a solution to the inequality. For example, the point (0, 0) (which is above the line) would satisfy the inequality, as would points like (4, 1), (5, 2), etc.

Final Graph:

You should now have a graph with a solid line representing y = (1/4)x - 3 and the area above the line shaded, indicating all the values of y that satisfy the original inequality.