Graph the inequality. y ≤ 4x + 2

Answer 1

To graph the inequality y ≤ 4x + 2, we'll first graph the equation y = 4x + 2, which represents the boundary line where the inequality holds as an equality. The inequality represents all the points below this boundary line and the line itself.

1. Identify the slope and y-intercept: The given equation is in the slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept. In this case, m = 4 and b = 2.

2. Plot the y-intercept: Since the y-intercept is 2, we'll put a point at the coordinates (0, 2) on the graph.

3. Use the slope to find another point on the line: The slope is 4, which means that for every 1 unit we move to the right on the x-axis, we move up 4 units on the y-axis. From the y-intercept point (0, 2), we move 1 unit to the right and 4 units up to find another point on the line, which is (1, 6).

4. Draw the boundary line: Connect the points (0, 2) and (1, 6) with a solid line, since the inequality includes the equal sign.

5. Shade the region below the line: Since the inequality is y ≤ 4x + 2, we want to shade all the points below the line. This shading represents all the points that satisfy the inequality.

Here's a graph of the inequality y ≤ 4x + 2: