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+9
y equals negative 3 x plus 9

y=−2x−3
y equals negative 2 x minus 3

y=−3x+3
y equals negative 3 x plus 3

y=3x−3

Answer 1

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

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept. Given that the slope \( m = -3 \), we can substitute this into the equation:

\[ y = -3x + b \]

Next, we will use the point (−2, 9) to find the value of \( b \). We plug in \( x = -2 \) and \( y = 9 \) into the equation:

\[ 9 = -3(-2) + b \]

Calculating \( -3(-2) \) gives us \( 6 \):

\[ 9 = 6 + b \]

To solve for \( b \), we subtract \( 6 \) from both sides:

\[ b = 9 - 6 \]

Thus:

\[ b = 3 \]

Now we can write the full equation for the linear function:

\[ y = -3x + 3 \]

Looking at the provided response options, we see that the correct linear function that matches our analysis is:

**y = −3x + 3**.