Choose the correct rule for the graph shown:

Question

A graph, likely representing a linear function, is displayed on a gridded coordinate plane. The x-axis ranges from -15 to 15, and the y-axis from -10 to 10. A straight line with a positive slope is drawn on the graph, originating near the origin (0,0) and extending into the positive quadrant.  The line passes through several points that are clearly visible on the grid. The grid lines are used to determine the locations of the points, to aid in understanding the function they represent.

Responses

y = 2x - 1
y = 2x - 1

y = 2x + 1
y = 2x + 1

y = 3x + 1
y = 3x + 1

y = 2x

Answer 1

To determine which of the given equations corresponds to the graph you've described, we need to analyze the information provided.

1. Positive Slope: The graph has a positive slope, which means the line rises as you move from left to right.

2. Originating Near the Origin (0,0): The line starts near the origin, indicating that the y-intercept might be close to 0.

3. Evaluating the Options:

   • y = 2x - 1: This line has a y-intercept of -1 and a slope of 2. It will not pass through the origin.

   • y = 2x + 1: This line has a y-intercept of +1 and a slope of 2. It will not pass through the origin.

   • y = 3x + 1: This line has a y-intercept of +1 and a slope of 3. It will not pass through the origin.

   • y = 2x: This line has a slope of 2 and passes through the origin (0,0).

Given the information, the most appropriate equation for the linear function represented by the graph, which has a positive slope and originates near the origin, is:

y = 2x