[tex]\underline{\underline{\large\bf{Solution:-}}}\\[/tex]
The standard form of a line is given by -
[tex]\green{ \underline { \boxed{ \sf{Ax+By=C}}}}[/tex]
where
- A= integer
- x = x-intercept
- B= integer
- y = y-intercept
- C = constant
Given Equation: -
[tex]\begin{gathered}\\\implies\quad \sf y = -\frac{5x}{4} -1 \\\end{gathered} [/tex]
Arranging equation in standard form -
[tex]\begin{gathered}\\\implies\quad \sf y = -\frac{5x}{4} - \frac{1}{1} \quad (1 = \frac{1}{1})\\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf y = -\frac{5x}{4} - \frac{1 \times 4}{1 \times 4} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf y = -\frac{5x}{4} - \frac{4}{4} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf y = \frac{-5x-4}{4} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 4y = -5x-4 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 4y +5x =-4 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 5x +4y=-4 \\\end{gathered} [/tex]
Comparing with standard form of line -
Thus , 5 is our required answer.
