Question

Analyze the linear function whose slope is -3 and passes through the coordinate pair (-2,9). Which linear function matches this line?
Y=-3x+3
Y=-2x-3
Y=-3x+9
Y=3x-3

Answer 1

To find the equation of the linear function with a slope of -3 that passes through the point (-2, 9), we can use the point-slope form of the equation of a line:

\[ y - y_1 = m(x - x_1) \]

where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope.

Given:
- Slope \( m = -3 \)
- Point \( (x_1, y_1) = (-2, 9) \)

Substituting these values into the point-slope form:

\[ y - 9 = -3(x - (-2)) \]
\[ y - 9 = -3(x + 2) \]

Now, distribute the -3:

\[ y - 9 = -3x - 6 \]

Next, isolate \( y \):

\[ y = -3x - 6 + 9 \]
\[ y = -3x + 3 \]

Now we can match this equation with the options provided.

The function we found is:
\[ y = -3x + 3 \]

Looking at the provided options:
1. \( Y = -3x + 3 \) (This is the correct answer)
2. \( Y = -2x - 3 \)
3. \( Y = -3x + 9 \)
4. \( Y = 3x - 3 \)

Thus, the matching linear function is **\( Y = -3x + 3 \)**.