The graph is showing which of the following functions?

(1 point)
Responses

y = −23x+2
\(y\ =\ -\frac{2}{3}x+2\) - no response given

y = 23x−2
\(y\ =\ \frac{2}{3}x-2\) - incorrect

y = −2x+3
\(y\ =\ -2x+3\) - no response given

y = −23x

1 answer

To determine which function corresponds to the graph, we'll need to analyze the slope and y-intercept of each option.

  1. y = −23x + 2: This function has a very steep slope of -23 and a y-intercept of +2.

  2. y = -\(\frac{2}{3}\)x + 2: This has a slope of -\(\frac{2}{3}\) and a y-intercept of +2. It's a bit less steep than the previous one.

  3. y = 23x - 2: This has a steep positive slope of 23 and a y-intercept of -2.

  4. y = \(\frac{2}{3}\)x - 2: This has a positive slope of \(\frac{2}{3}\) and a y-intercept of -2.

  5. y = −2x + 3: This has a slope of -2 and a y-intercept of +3.

  6. y = −23x: This has a very steep slope of -23 and a y-intercept of 0 (since the constant term is absent).

To identify the correct function, you would need to look at the steepness of the graph and its intersection point with the y-axis (the y-intercept).

  • If the graph has a steep downward slope and intersects at y = 2, then it would correspond to the first option (y = −23x + 2).
  • If it has a less steep slope and intersects at y = 2, then the second option (y = -\(\frac{2}{3}\)x + 2) fits.
  • If it has a steeper positive slope and intersects at y = -2, the third option (y = 23x - 2) is correct, and so forth.

Without the graph, I can't definitively tell which function it corresponds to, but you can analyze the intersection and slope as described to find the right match.