Respuesta :
The equation of a line is given by,
[tex]ax+by=4\text{ ---(1)}[/tex]The general equation of a line is given by,
[tex]y=mx+c\text{ ---(2)}[/tex]Here, m is the slope of the line and c is the y intercept.
Rewrite equation (1) into the form of equation (2).
[tex]\begin{gathered} by=-ax+4 \\ y=\frac{-a}{b}x+\frac{4}{b}\text{ ---(3)} \end{gathered}[/tex]Comparing equations (2) and (3), the slope of the line is
m=-a/b and the y intercept c=4/b
a)
A line is parallel to the x axis when the slope is equal to zero.
Therefore, the given line is parallel to the x axis if,
[tex]\begin{gathered} m=0 \\ \frac{-a}{b}=0 \\ a=0 \end{gathered}[/tex]Since y intercept c=4/b , b cannot be zero.
So, the given line is parallel to the x axis when a=0 and b≠0.
b)
The line is parallel to the y axis when the slope is undefined.
When the line is parallel to the y axis, the x intercept can be found by putting y=0 in equation (1).
[tex]x=\frac{4}{a}[/tex]The given line is parallel to the y axis when b=0 and a≠0.
c)
Given, the slope of line is m= 5/8.
From equation (2), the slope of line is m=-a/b.
Therefore,
[tex]\begin{gathered} \frac{-a}{b}=\frac{5}{8} \\ \frac{a}{b}=\frac{-5}{8} \end{gathered}[/tex]Therefore, we can take a=-5 and b=8 when the line has slope 5/8.
