Question

Which equation matches the graph?

A. y - 2= 3(× -2)
B. y - 2= 3(×+2)
C. y + 2= -3(×+2)
D. y - 2= -3(x-2)
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Answer 1

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Answer 2

based on the slope and the y-intercept, the correct equation that matches the graph is:

D.
`\( y - 2 = -3(x - 2) \)`

To determine which equation matches the graph, we need to analyze the slope and the y-intercept of the line shown in the graph.

Looking at the graph, we can observe the following characteristics:

1. The line is decreasing, which means it has a negative slope.

2. The line crosses the y-axis (the vertical axis) at the point (0, 2), which gives us the y-intercept.

Now, let's analyse the equations to see which one matches these characteristics:

A.
`\( y - 2 = 3(x - 2) \)` - This equation suggests a positive slope (upwards) since 3 is positive, which does not match the graph.

B.
`\( y - 2 = 3(x + 2) \)` - This also suggests a positive slope and does not match.

C.
`\( y + 2 = -3(x + 2) \)` - This equation has a negative slope, which matches the graph, but the y-intercept is incorrect since it suggests the line crosses the y-axis at (0, -2).

D.
`\( y - 2 = -3(x - 2) \)` - This has a negative slope, and the y-intercept is correct, so it matches the graph.

Therefore, based on the slope and the y-intercept, the correct equation that matches the graph is:

D.
`\( y - 2 = -3(x - 2) \)`