Which equations could represent this graph? Choose all that apply.

y = -2/3x + 5
y = -2/3x + 5

y = 5x - 2
y = 5x - 2

2x + 3y = 15
2x + 3y = 15

-3x + 2y = 5
-3x + 2y = 5

y = 5x + 8

1 answer

To determine which equations could represent the graph you're referring to, we need to analyze the provided equations. However, since I cannot see the graph, I will help you evaluate the equations based on their slopes and y-intercepts.

  1. y = -2/3x + 5

    • Slope: -2/3
    • Y-intercept: 5
  2. y = 5x - 2

    • Slope: 5
    • Y-intercept: -2
  3. 2x + 3y = 15

    • Rearranged to slope-intercept form:
      • 3y = -2x + 15
      • y = -2/3x + 5
    • Slope: -2/3
    • Y-intercept: 5
  4. -3x + 2y = 5

    • Rearranged to slope-intercept form:
      • 2y = 3x + 5
      • y = (3/2)x + 5/2
    • Slope: 3/2
    • Y-intercept: 5/2
  5. y = 5x + 8

    • Slope: 5
    • Y-intercept: 8

Summary:

  • y = -2/3x + 5 and 2x + 3y = 15 are equivalent and have the same slope and y-intercept.
  • y = 5x - 2 and y = 5x + 8 have a slope of 5.
  • -3x + 2y = 5 has a different slope and intercept.

To choose which equations could represent the graph, consider the slope and y-intercept you see in the graph:

  • If the graph has a slope of -2/3 and a y-intercept of 5, select y = -2/3x + 5 and 2x + 3y = 15.
  • If the graph has a slope of 5, select y = 5x - 2 and y = 5x + 8.

Without knowing the specifics of the graph, you would select the equations based on the characteristics observed in the graph.

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