Question 960152
When they say " the graph is a vertical line" that
is the same as saying the slope is infinite
Slope = [ change in y ] / change in x ]
If there is zero change in {{{ x }}}, then
slope = [ delta y ] / 0
slope = infinity
The equation becomes {{{ x = k }}} because
{{{ y }}} can be anything, but {{{ x }}} is whatever
value you pick for it ( whatever {{{ k }}} )
Suppose I say {{{ x = 7 }}} then
{{{ y = -(A/B)*x + C }}}
{{{ y = -(A/B)*7 + C }}}
{{{ B }}} approaches zero, so
{{{ y }}} cannot be determined
Note that this vertical line is NOT a function.
A function must have a unique {{{ y }}} for
any {{{ x }}} that you choose.
------------------------------
A horizontal line means slope = {{{ 0 }}}
{{{ y = -(A/B)*x + C }}}
{{{ -(A/B) = 0 }}}
so, {{{ y = C }}}
is the equation
You can't pick any {{{ y }}}, the equation already says
{{{ y = C }}}
This line is a function, since any {{{ x }}} chosen
gives me a unique {{{ y }}} ( It's always the same {{{ y }}},
but I don't get MORE than one {{{ y }}}
-------------------
Hope this helps
-----------------------------------------