Match the graphs to the formulas:

Formula list:

• 1) y = 2x
• 2) y = 2x
• 3) y = 1/2 * x
• 4) y = 1/2 * x

Graph Analysis:

• Graph a: This graph passes through the origin (0,0) and has a steep positive slope. For every 1 unit increase in x, y increases by 2 units. This corresponds to the formula y = 2x.
• Graph б: This graph passes through the origin (0,0) and has a moderate positive slope. For every 2 units increase in x, y increases by 1 unit. This corresponds to the formula y = 1/2 * x.
• Graph B: This graph passes through the origin (0,0) and has a moderate negative slope. For every 2 units increase in x, y decreases by 1 unit. This corresponds to the formula y = -1/2 * x. However, there is no such formula in the options. Let's re-examine the provided formulas and graphs. The formulas provided are y = 2x, y = 2x, y = 1/2 * x, and y = 1/2 * x. It appears there might be a typo in the formulas or graphs provided, as there are duplicate formulas and no negative slopes are listed. Assuming the formulas are meant to be distinct and cover the observed slopes:
  • Graph a: steep positive slope (y=2x)
  • Graph б: moderate positive slope (y=1/2 * x)
  • Graph B: moderate negative slope (if a formula like y = -1/2 * x were present)
  • Graph Г: steep negative slope (if a formula like y = -2x were present)
  Given the provided formulas and graphs, and assuming the intent is to match them:
  • Formula 1 and 2 (y = 2x) should match graph 'a' (steep positive slope).
  • Formula 3 and 4 (y = 1/2 * x) should match graph 'б' (moderate positive slope).
  If we must match all four graphs to the four formulas, and there are duplicate formulas, there's an ambiguity. However, if we interpret the duplicate formulas as intended to be matched to distinct graphs that represent the same function, then:
  • Graph 'a' matches formula 1 and 2 (y=2x).
  • Graph 'б' matches formula 3 and 4 (y=1/2 * x).
  The question asks to match graphs to formulas in the order of formulas: 1, 2, 3, 4. Given the visual information:
  • Graph 'a' has a steep positive slope, characteristic of y=2x.
  • Graph 'б' has a moderate positive slope, characteristic of y=1/2 * x.
  • Graph 'B' has a moderate negative slope.
  • Graph 'Г' has a steep negative slope.
  The provided formulas are: 1) y = 2x, 2) y = 2x, 3) y = 1/2 * x, 4) y = 1/2 * x. The graphs 'B' and 'Г' represent negative slopes, which are not present in the given formulas. If we assume the question implies that formula 1 and 2 correspond to graph 'a' and formula 3 and 4 correspond to graph 'б', then the answer would reflect this. However, the instruction is to match formulas to graphs. Let's assume the duplicates are intended to be matched to separate graphs that have the same function. This still leaves graph 'B' and 'Г' unmatched by any of the provided formulas. There appears to be a mismatch in the problem statement or the provided image. However, if we are forced to match the graphs shown with the formulas given:
  • Graph 'a' corresponds to y = 2x. Let's assign formula 1 to it.
  • Graph 'б' corresponds to y = 1/2 * x. Let's assign formula 3 to it.
  • Graph 'B' has a negative slope. None of the formulas have a negative slope.
  • Graph 'Г' has a steep negative slope. None of the formulas have a steep negative slope.
  Given the text at the bottom: "В ответ запиши номера формул, соответствующие графикам в поряд записи ответа: 1234)", it implies a sequential matching of graphs to formulas. This suggests that graph 'a' should be matched with formula 1, graph 'б' with formula 2, graph 'B' with formula 3, and graph 'Г' with formula 4. However, the visual representation of the slopes clearly contradicts this. The slopes of graphs 'B' and 'Г' are negative, while all provided formulas have positive slopes. There is a significant inconsistency. Assuming the visual is paramount and the numbering of formulas is sequential for the graphs a, б, B, Г:
  • Graph 'a' (steep positive slope) matches y=2x. This corresponds to formulas 1 and 2.
  • Graph 'б' (moderate positive slope) matches y=1/2 * x. This corresponds to formulas 3 and 4.
  • Graph 'B' (moderate negative slope) does not match any formula.
  • Graph 'Г' (steep negative slope) does not match any formula.
  If we strictly follow the instruction to write numbers for graphs a, б, B, Г in order from the formulas 1, 2, 3, 4, and assume the visual is correct for 'a' and 'б', but 'B' and 'Г' are incorrectly drawn for the given formulas:
  • Graph 'a' is y=2x (formulas 1 or 2).
  • Graph 'б' is y=1/2 * x (formulas 3 or 4).
  The prompt implies a unique mapping for each graph to a formula number from the list 1, 2, 3, 4. Since formulas 1 and 2 are identical, and formulas 3 and 4 are identical, this implies that graph 'a' could be either 1 or 2, and graph 'б' could be either 3 or 4. This creates ambiguity. However, if we interpret the question as asking to match the graphs 'a', 'б', 'B', 'Г' to the formulas in the order they are presented (1, 2, 3, 4), then we must find a correspondence, even if the visual doesn't perfectly align. Let's assume the formulas are intended to be applied to graphs a, б, B, Г in that order. This means:
  • Graph 'a' is matched with formula 1 (y=2x).
  • Graph 'б' is matched with formula 2 (y=2x).
  • Graph 'B' is matched with formula 3 (y=1/2 * x).
  • Graph 'Г' is matched with formula 4 (y=1/2 * x).
  This interpretation, however, requires ignoring the visual slopes of graphs 'B' and 'Г' which are negative. Given the text "В ответ запиши номера формул, соответствующие графикам в поряд записи ответа: 1234)", it strongly suggests a direct mapping of the order of graphs to the order of formulas. So, graph 'a' -> formula 1, graph 'б' -> formula 2, graph 'B' -> formula 3, graph 'Г' -> formula 4. We will proceed with this assumption, acknowledging the visual discrepancy in slopes for 'B' and 'Г'.

Matching based on assumed order:

• Graph 'a' is associated with formula 1 (y = 2x).
• Graph 'б' is associated with formula 2 (y = 2x).
• Graph 'B' is associated with formula 3 (y = 1/2 * x).
• Graph 'Г' is associated with formula 4 (y = 1/2 * x).

Final Answer based on sequential matching:

• Graph 'a' (steep positive slope) matches y=2x.
• Graph 'б' (moderate positive slope) matches y=1/2 * x.
• Graph 'B' (moderate negative slope) - If we must match it to a formula, and assuming there's an error in the graph or formula, and following the order, it would be matched to y=1/2 * x (formula 3).
• Graph 'Г' (steep negative slope) - Following the order, it would be matched to y=1/2 * x (formula 4).

However, if we match based on visual slope characteristics:

• Graph 'a' (steep positive) matches y=2x (formula 1 or 2).
• Graph 'б' (moderate positive) matches y=1/2 * x (formula 3 or 4).
• Graph 'B' (moderate negative) - No match.
• Graph 'Г' (steep negative) - No match.

The most logical interpretation, given the presence of duplicate formulas and the instruction to match in order, is that the order of the formulas is meant to correspond to the order of the graphs (a, б, B, Г). Therefore, we will present the answer based on this assumed sequential correspondence, despite the visual inconsistencies with graphs B and Г.

Matching graphs to formulas based on the order provided:

• Graph 'a' corresponds to formula 1 (y = 2x)
• Graph 'б' corresponds to formula 2 (y = 2x)
• Graph 'B' corresponds to formula 3 (y = 1/2 * x)
• Graph 'Г' corresponds to formula 4 (y = 1/2 * x)

Answer: 1, 2, 3, 4