Which graph represents the given inequality? y > 5x – 1 (1 point) Responses Image with alt text: A coordinate plane with a dashed boundary line graphed with a y intercept of negative 1 and slope of 5. Shading is above the boundary line. Image with alt text: A coordinate plane with a dashed boundary line graphed with a y intercept of negative 5 and slope of 1. Shading is below the boundary line. Image with alt text: A coordinate plane with a dashed boundary line graphed with a y intercept of negative 5 and slope of 1. Shading is below the boundary line.
The correct graph that represents the given inequality is the first option: "A coordinate plane with a dashed boundary line graphed with a y intercept of negative 1 and slope of 5. Shading is above the boundary line."
The correct graph representing the given inequality y > 5x – 1 is the first option:
Image with alt text: A coordinate plane with a dashed boundary line graphed with a y intercept of negative 1 and slope of 5. Shading is above the boundary line.
To determine which graph represents the inequality y > 5x - 1, we need to understand the equation and how it relates to a graph.
The inequality y > 5x - 1 represents all the points (x, y) on a graph where y is greater than 5 times x minus 1.
To graph this inequality, we need to first plot the boundary line y = 5x - 1. This line separates the coordinate plane into two regions: one region where y is greater than 5x - 1, and another region where y is less than or equal to 5x - 1.
Next, we need to determine whether to shade the region above or below the boundary line to represent the inequality y > 5x - 1. To do this, we can pick a point not on the boundary line and substitute its x and y values into the inequality. If the inequality is true, then we shade the region containing that point; otherwise, we shade the other region.
Let's evaluate the inequality by choosing a simple point such as (0,0):
- Substitute x = 0 and y = 0 into the inequality: 0 > 5(0) - 1
- Simplify: 0 > 0 - 1
- Simplify further: 0 > -1
Since the inequality is true, we need to shade the region above the boundary line.
Based on the given options:
- The first option (image with alt text: A coordinate plane with a dashed boundary line graphed with a y intercept of negative 1 and slope of 5. Shading is above the boundary line) correctly represents the inequality y > 5x - 1.
Therefore, the first graph is the correct representation of the given inequality.