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.