ANSWER:
The line equation with the slope [tex]\frac{-2}{9}[/tex] and the y-intercept (0,2) is 2x + 9y – 18 = 0.
SOLUTION:
Given, slope of the line is [tex]\frac{-2}{9}[/tex] and point on the line (0, 2).
We have to find the line equation.
As we have slope and a point, let us find the point slope form of the given equation.
Point slope form → [tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
Where m is slope and [tex]\left(x_{1}, y_{1}\right)[/tex] is a point on that line
Here, in our problem, [tex]\mathrm{m}=-\frac{2}{9} \text { and }\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)=(0,2)[/tex]
Now, we get
[tex]\begin{array}{l}{y-2=-\frac{2}{9}(x-0)} \\\\ {y-2=-\frac{2}{9} x}\end{array}[/tex]
9(y – 2) = -2x
9y – 18 = -2x
2x + 9y – 18 = 0
Hence, the line equation is 2x + 9y – 18 = 0.
