Question

Analyze the linear function whose slope is −3
and passes through the coordinate pair (−2,9)
. Which linear function matches this line?(1 point)
Responses

y=−3x+3
y equals negative 3 x plus 3

y=−2x−3
y equals negative 2 x minus 3

y=3x−3
y equals 3 x minus 3

y=−3x+9

Answer 1

To determine the linear function given the slope and a point, we can use the point-slope form of a linear equation, which is:

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

Here, \( m \) is the slope and \( (x_1, y_1) \) is the point through which the line passes. In your case:

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

Now, plug in the values:

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

Now, simplify the equation:

1. Distribute \(-3\):

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

2. Add \(9\) to both sides:

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

\[ y = -3x + 3 \]

Thus, the linear function that matches this line is:

\[ y = -3x + 3 \]

Therefore, the correct response from your options is:

**y = −3x + 3**.