Option 1
The equation of line in standard form passing through point (0, 5) is 5x – 9y = - 45
Solution:
Given that slope "m" = [tex]\frac{5}{9}[/tex]
The lines passes through point (0, 5)
We have to write the equation of line in standard form
The standard form of an equation is Ax + By = C
Now first let use point slope form to find equation of line and then convert to standard form.
[tex]\begin{array}{l}{\text { The point slope form is } y-y_{1}=m\left(x-x_{1}\right)} \\\\ {\text { Here } m=\frac{5}{9} ; x_{1}=0 ; y_{1}=5}\end{array}[/tex]
[tex]\rightarrow y-5=\frac{5}{9}(x-0)[/tex]
Converting to standard form by rearranging terms,
9(y - 5) = 5(x – 0 )
9y – 45 = 5x
5x – 9y = - 45
Hence, the line equation is 5x – 9y = - 45, so option 1 is correct.
