Analyze the linear function whose slope is −3 and passes through the coordinate pair (−2,9) . Which linear function matches this line?(1 point)Responsesy=−2x−3y equals negative 2 x minus 3y=−3x+3y equals negative 3 x plus 3y=3x−3y equals 3 x minus 3y=−3x+9

Answer 1

To analyze the linear function given 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 which is:

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

Where:

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

Substituting the given values:

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

We get:

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

Now, simplifying this equation:

1. Distribute the slope on the right side:

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

2. Add 9 to both sides:

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

\[ y = -3x + 3 \]

Now that we have the equation in slope-intercept form (y = mx + b), we can more directly see that the equation is:

\[ y = -3x + 3 \]

Now let's look at the responses to find which matches:

1. \( y = -2x - 3 \)
2. \( y = -3x + 3 \)
3. \( y = 3x - 3 \)
4. \( y = -3x + 9 \)

The correct response that matches the derived linear function is:

\( y = -3x + 3 \).