Video Transcript
Which of the following equations
represents a straight line? (A) π¦ equals root π₯ plus six, (B)
π¦ plus one over π₯ equals negative eight, (C) π₯ plus root π¦ equals negative five,
or (D) negative seven π₯ minus two π¦ equals negative nine.
So to enable us to decide which one
of these is in fact the correct equation to represent a straight line, what weβre
gonna do is look at a couple of the general forms for the equation of a straight
line. Well, the couple of forms that
weβve got here are the standard form, π΄π₯ plus π΅π¦ equals πΆ, or we have the
point-slope form, which is π¦ minus π¦ sub one equals π multiplied by π₯ minus π₯
sub one.
Well, one thing we can notice from
both of our forms is the fact that we have here π₯ to the power of one and then π¦
to the power of one. And thatβs in the standard
form. And then in the point-slope form,
we also have π¦ to the power of one or π₯ to the power of one. So therefore, with this bit of
information and the two forms we have here for the equation of a straight line,
letβs have a look at the four equations that we have to see if they in fact
represent a straight line.
Well, if we look at equation (A),
what we have is root π₯. Well, if we write this in exponent
form, this is π₯ to the power of a half. So therefore, this cannot be the
correct answer cause this will not represent a straight line.
Well, in equation (B), what we have
is one over π₯. Well, if we rewrite this in
exponent form, this is π₯ to the power of negative one. So therefore, once again, this
cannot be the correct answer. And it cannot be a straight line
because we donβt have the π₯ to the power of one, π¦ to the power of one.
Then, if we take a look at (C),
once again, weβve got a root, and this time itβs root π¦. So therefore, this is gonna be π¦
to the power of a half. So therefore, this canβt be the
correct equation either.
But if we check equation (D), what
we have here is π₯ to the power of one and π¦ to the power of one. So therefore, this can be the
correct equation. So this could be the equation of a
straight line. And what we can also notice is that
it takes the standard form for the equation of a straight line, and that is π΄π₯
plus π΅π¦ equals πΆ. So therefore, we can say that the
equation which represents the straight line is negative seven π₯ minus two π¦ equals
negative nine. And itβs in the standard form π΄π₯
plus π΅π¦ equals πΆ, where π΄ is equal to negative seven, π΅ is equal to negative
two, and πΆ is equal to negative nine. Okay, great, so weβve solved this
problem.