68. Analyzing a Line A line is represented by the equation ax+by=4 . (a) When...

First, write the equation of line ${\displaystyle ax+by=4}$ in slope-intercept form, that is in the form of ${\displaystyle y=mx+c}$; here, m is the slope and c is the y-intercept of the line.
${\displaystyle ax+by=4}$
${\displaystyle by=-ax+4}$
${\displaystyle y=\frac{ax}{b}+\frac{4}{b}}$
On comparing the above equation of line with standard slope-intercept form of line, the slope m is ${\displaystyle -\frac{a}{b}}$.
The line is parallel of x-axis when the slope of the line is 0.
Apply the condition that the line is parallel of x-axis when the slope of the line is 0, that is ${\displaystyle m=0}$. Here, ${\displaystyle m=-\frac{a}{b}}$.
${\displaystyle m=0}$
${\displaystyle -\frac{a}{b}=0}$
${\displaystyle a=0}$
Thus, the line ${\displaystyle ax+by=4}$ is parallel to x-axis when a=0.