To determine which equations could represent the graph, we need to analyze each equation to see if they match the characteristics such as slope or y-intercept, or any specific points they may go through.
-
y = 5x - 2: This equation has a slope of 5 and a y-intercept of -2.
-
y = -2/3x + 5: This equation has a slope of -2/3 and a y-intercept of 5.
-
2x + 3y = 15: Rearranging this equation into slope-intercept form (y = mx + b) gives us y = -2/3x + 5. Therefore, this equation is equivalent to the second option.
-
-3x + 2y = 5: Rearranging this equation into slope-intercept form gives y = (3/2)x + 5/2. This equation has a different slope and y-intercept.
-
y = 5x + 8: This equation has a slope of 5 and a y-intercept of 8.
Based on this analysis, the valid equations that could potentially represent the graph are:
- y = 5x - 2
- y = -2/3x + 5
- 2x + 3y = 15
Thus, the answers are: y = 5x - 2, y = -2/3x + 5, and 2x + 3y = 15.