Answer
a) a = 0 or -$\frac{a}{b}$ = 0.
b) b = 0.
c) a = -5, b = 8
d) a = 5, b = 2
e) a = $\frac{5}{2}$ and b = $3}$
Work Step by Step
Writing equation in slope intercept form:
ax + by = 4
y = -$\frac{a}{b}$x + $\frac{4}{b}$
a) line will be parallel to x axis if it's slope is 0
So,
-$\frac{a}{b}$ = 0 or a = 0.
b) line will be parallel to y axis if it's slope is undefined i.e.
-$\frac{a}{0}$ = undefined
b = 0.
c) if we put a = -5 and b = 8
-5x + 8y = 4
slope intercept form:
y = $\frac{5}{8}$x + $\frac{1}{2}$
d) line perpendicular to y = $\frac{2}{5}$x +3 will have slope -$\frac{5}{2}$
if we put a = 5 and b = 2, we get:
5x + 2y = 4
slope intercept form
y = -$\frac{5}{2}$x +2
which has slope of -$\frac{5}{2}$
e) if we put a = $\frac{5}{2}$ and b = $3$
$\frac{5}{2}$x + $\frac{6}{2}$y = 4
5x + 6y = 8
