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=3x−3
y equals 3 x minus 3

y=−3x+3
y equals negative 3 x plus 3

y=−3x+9
y equals negative 3 x plus 9

y=−2x−3
y equals negative 2 x minus 3

Answer 1

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

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

where \(m\) is the slope and \((x_1, y_1)\) is the point the line passes through.

Given:

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

Substituting into the point-slope equation:

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

Simplifying:

\[ y - 9 = -3(x + 2) \] \[ y - 9 = -3x - 6 \] \[ y = -3x + 3 \]

Now we compare this equation to the given options:

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

The correct linear function that matches this line is:

\(y = -3x + 3\)

So, the answer is: y equals negative 3 x plus 3.