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

(2 points)
Responses

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

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

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

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

y = 5x + 8

1 answer

To determine which equations could represent the graph, we need to assess the slope and y-intercept of each equation and compare them with the characteristics of the given graph.

Here are the equations reviewed:

  1. y = -2/3x + 5: This has a negative slope (-2/3) and a y-intercept of 5.

  2. 2x + 3y = 15: Rearranging into slope-intercept form (y = mx + b): \[ 3y = -2x + 15 \implies y = -\frac{2}{3}x + 5 \] This has the same slope and intercept as the first equation, so it is equivalent.

  3. -3x + 2y = 5: Rearranging into slope-intercept form: \[ 2y = 3x + 5 \implies y = \frac{3}{2}x + \frac{5}{2} \] This has a positive slope (3/2) and is unlikely to match with a graph with a negative slope.

  4. y = 5x - 2: This has a positive slope (5) and a negative y-intercept (-2). This will not match with any negative slope graph.

  5. y = 5x + 8: This also has a positive slope (5) and a positive y-intercept (8), which again does not match with any negative slope graph.

Based on this analysis:

  • The equations that could represent the graph, assuming it has a negative slope and an intercept of 5, are:
    • y = -2/3x + 5
    • 2x + 3y = 15

The equations that do not match are:

  • -3x + 2y = 5
  • y = 5x - 2
  • y = 5x + 8

Final answer: y = -2/3x + 5 and 2x + 3y = 15.