To find the equation of a line given a slope and a y-intercept, you can use the slope-intercept form of a linear equation. The slope-intercept form is given by:
[tex]\[ y = mx + b \][/tex]
Here, [tex]\( m \)[/tex] represents the slope of the line and [tex]\( b \)[/tex] represents the y-intercept, which is the point where the line crosses the y-axis.
In the given problem, the slope ([tex]\( m \)[/tex]) is [tex]\(-\frac{2}{9}\)[/tex] and the y-intercept ([tex]\( b \)[/tex]) is 3.
Let's substitute these values into the slope-intercept formula:
[tex]\[ y = \left( -\frac{2}{9} \right) x + 3 \][/tex]
We can convert [tex]\(-\frac{2}{9}\)[/tex] into its decimal form to get a more straightforward representation if needed. The fraction [tex]\(-\frac{2}{9}\)[/tex] is equal to approximately -0.2222222222222222. Substituting the decimal form into the equation would look like this:
[tex]\[ y = (-0.2222222222222222) x + 3 \][/tex]
Therefore, the equation of the line with a slope of [tex]\(-\frac{2}{9}\)[/tex] and a y-intercept of 3 is:
[tex]\[ y = (-0.2222222222222222) x + 3 \][/tex]
