Analyze the linear function whose slope is −3

Question

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

y=−2x−3
y equals negative 2 x minus 3

y=−3x+9
y equals negative 3 x plus 9

y=3x−3
y equals 3 x minus 3

y=−3x+3

Answer 1

To analyze the linear function with a slope of -3 that passes through the point (-2, 9), we can use the point-slope form of a linear equation, which is given by:

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

Where \( (x_1, y_1) \) is the point the line passes through and \( m \) is the slope. In this case:

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

Substituting these values into the point-slope formula:

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

This simplifies to:

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

Now distribute the -3:

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

Next, add 9 to both sides:

\[ y = -3x + 3 \]

So the linear function that matches the line is:

y = -3x + 3.

Therefore, the correct response is:

y = −3x + 3.