To determine a linear equation given a y-intercept and a slope, we rely on the standard form of a linear equation:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] denotes the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept, or the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is 0.
Given:
1. The slope ([tex]\( m \)[/tex]) is -3.
2. The y-intercept ([tex]\( b \)[/tex]) 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.
[tex]\[ y = mx + b \][/tex]
Substitute [tex]\( m = -3 \)[/tex] and [tex]\( b = 9 \)[/tex]:
[tex]\[ y = -3x + 9 \][/tex]
Thus, the linear equation that has a y-intercept of (0, 9) and a slope of -3 is:
[tex]\[ y = -3x + 9 \][/tex]
So, the final equation is:
[tex]\[ y = -3x + 9 \][/tex]
