Question

y ≥ -5x - 4

Explanation:

Step1: Analyze the inequality

The inequality is \( y \geq -5x - 4 \). First, we need to graph the boundary line \( y = -5x - 4 \). Since the inequality is "greater than or equal to", the line should be solid (not dashed).

Step2: Find the slope and y-intercept

For the line \( y = -5x - 4 \), the slope \( m = -5 \) and the y-intercept \( b = -4 \). So, we start by plotting the y-intercept at \( (0, -4) \).

Step3: Use the slope to find another point

The slope \( -5 \) can be written as \( \frac{-5}{1} \). From the y-intercept \( (0, -4) \), we move down 5 units and right 1 unit to get the point \( (1, -9) \), or up 5 units and left 1 unit to get the point \( (-1, 1) \). Let's use \( (-1, 1) \) for easier plotting on the given grid.

Step4: Draw the boundary line

Connect the points \( (0, -4) \) and \( (-1, 1) \) with a solid line (since the inequality is \( \geq \)).

Step5: Shade the region

To determine which side to shade, we can test a point not on the line. Let's use the origin \( (0, 0) \). Substitute \( x = 0 \) and \( y = 0 \) into the inequality: \( 0 \geq -5(0) - 4 \), which simplifies to \( 0 \geq -4 \). This is true, so we shade the region that includes the origin (above the line, since the line has a negative slope and we tested the origin which is above the line \( y = -5x - 4 \) when \( x = 0 \)).

Answer:

To graph \( y \geq -5x - 4 \):

1. Plot the y - intercept at \( (0, - 4) \) and use the slope \( - 5 \) to find another point (e.g., \( (-1, 1) \)).
2. Draw a solid line through these points (because of the "≥" symbol).
3. Shade the region above the line (since the test point \( (0,0) \) satisfies the inequality, and it lies above the line).