Question

1. graph the inequality on the axes below.

$y \geq \frac{3}{5}x + 3$

Explanation:

Step1: Identify the boundary line

The inequality is \( y \geq \frac{3}{5}x + 3 \). First, graph the boundary line \( y=\frac{3}{5}x + 3 \). The slope \( m=\frac{3}{5} \) and the y - intercept \( b = 3 \). Plot the y - intercept at \( (0,3) \). Then, use the slope to find another point: from \( (0,3) \), move up 3 units and right 5 units to get \( (5,6) \) (or down 3 units and left 5 units to get \( (- 5,0) \)). Since the inequality is \( \geq \), the boundary line should be solid (because the inequality includes equality).

Step2: Determine the shading region

To find which side of the line to shade, we can test a point not on the line. A common test point is the origin \( (0,0) \). Substitute \( x = 0 \) and \( y=0 \) into the inequality: \( 0\geq\frac{3}{5}(0)+3\), which simplifies to \( 0\geq3 \). This is false. So we shade the side of the line that does not include the origin. In other words, we shade the region above the line \( y = \frac{3}{5}x+3 \) (since the test point below the line gave a false statement, we shade above).

Answer:

1. Draw a solid line through the points \((0, 3)\) and \((5, 6)\) (or other points determined by the slope - intercept form \(y=\frac{3}{5}x + 3\)).
2. Shade the region above the solid line.