To determine a linear equation given a y-intercept and a slope, we rely on the standard form of a linear equation:
\(\[ y = mx + b \]\)
where:
- \(\( m \)\) denotes the slope of the line.
- \(\( b \)\) is the y-intercept, or the value of \(\( y \)\) when \(\( x \)\) is 0.
Given:
1. The slope (\(\( m \)\)) is -3.
2. The y-intercept (\(\( b \)\)) is 9 (this means the line crosses the y-axis at the point (0, 9)).
We just need to substitute these values into the standard linear equation form.
\(\[ y = mx + b \]\)
Substitute \(\( m = -3 \)\) and \(\( b = 9 \)\):
\(\[ y = -3x + 9 \]\)
Thus, the linear equation that has a y-intercept of (0, 9) and a slope of -3 is:
\(\[ y = -3x + 9 \]\)
So, the final equation is:
\(\[ y = -3x + 9 \]\)
