Question 74425
Given any 2 points, you can draw a line through them, and
that line will have a certain slope.
What's the definition of slope?
It is slope = (change in y) / (change in x) or
slope = (change in vertical) / )change in horizontal) same thing
So how do you find these?
When you're given 2 points, you can call them {{{P[1]}}} and {{{P[2]}}}
Then you can say {{{P[1]}}} = ({{{x[1]}}},{{{y[1]}}})
and also can say {{{P[2]}}} = ({{{x[2]}}},{{{y[2]}}})
The change in y is {{{y[2]}}} - {{{y[1]}}}
The change in x is {{{x[2]}}} - {{{x[1]}}}
Now just plug in the numbers in the problem
{{{P[1]}}} = ({{{-1}}},{{{-2}}})
{{{P[2]}}} = ({{{-1}}},{{{1}}})
Change in y = {{{1}}} - {{{-2}}}
change in x = {{{-1}}} - {{{-1}}}
slope = (change in y) / (change in x)
slope = {{{(1 - (-2)) / (-1 - (-1))}}}
slope = {{{3 / 0}}}
What does this tell you? First, dividing by 0 is not allowed, but
the 0 tells you that there is no change in x since you're
subtracting -1 from -1.
No change in x means the line is vertical.
If there were no change in y, the line would be horizontal
The slope of a vertical line is infinity
Pick any point on this line. x will be -1 no matter what
y is. So, the equation of the line is {{{x = -1}}}