Match the graphs with the formulas.

Graphs and Formulas

The task is to match the given linear functions (formulas) with their corresponding graphical representations.

• Graph 'a' shows a line passing through the origin with a steep positive slope. This corresponds to a function where y increases rapidly as x increases.
• Graph 'б' shows a line passing through the origin with a gentle positive slope. This corresponds to a function where y increases slowly as x increases.
• Graph 'в' shows a line passing through the origin with a gentle negative slope. This corresponds to a function where y decreases slowly as x increases.
• Graph 'г' shows a line passing through the origin with a steep negative slope. This corresponds to a function where y decreases rapidly as x increases.

Let's analyze the formulas:

1. y = 2x: This is a linear function with a slope of 2 and a y-intercept of 0. The slope is positive and steep.
2. y = -2x: This is a linear function with a slope of -2 and a y-intercept of 0. The slope is negative and steep.
3. y = -1/2x: This is a linear function with a slope of -1/2 and a y-intercept of 0. The slope is negative and gentle.
4. y = 1/2x: This is a linear function with a slope of 1/2 and a y-intercept of 0. The slope is positive and gentle.

Matching the graphs to the formulas:

• Graph 'a' matches with formula 1) y = 2x (steep positive slope).
• Graph 'б' matches with formula 4) y = 1/2x (gentle positive slope).
• Graph 'в' matches with formula 3) y = -1/2x (gentle negative slope).
• Graph 'г' matches with formula 2) y = -2x (steep negative slope).