The equation y = 8.1x models the relationship between the number of hours Alexander works, x, and the dollar amount he earns, y. Which is the graph of the equation y = 8.1x?A coordinate grid with a curved line starting at (1, 8) curving down and to the right passing through (2, 4), (4, 2), and (7, 1)A coordinate grid with a straight line starting at (0, 0) and (1, 8).A coordinate grid with a straight line starting at (0, 2) passing through (2, 4) and (6, 8).

Question

GPT-4o mini · Accepted Answer

The equation $ y = 8.1x $ represents a linear relationship between $ x $ and $ y $, where the slope is $ 8.1 $. This means that for every hour Alexander works, he earns $8.10. To find the correct graph of this linear equation, we should check for the following characteristics: 1. The line should pass through the origin (0,0) because when $ x = 0 $, $ y $ should also be 0. 2. The slope of the line should indicate that for every increase of 1 in $ x $, $ y $ increases by 8.1. Now, let’s evaluate the options: 1. **Curved line**: This option does not represent a linear equation, so it cannot be correct. 2. **Straight line starting at (0, 0) and passing through (1, 8)**: This option is consistent with the equation $ y = 8.1x $. If $ x = 1 $, then $ y = 8.1 \cdot 1 = 8.1 $, which is very close to 8 (though not matching exactly unless rounded). 3. **Straight line starting at (0, 2)**: This option cannot be correct because the line does not start at the origin. The best option that matches the expected graph of the equation $ y = 8.1x $ is the second one: **A coordinate grid with a straight line starting at (0, 0) and passing through (1, 8)**.