# Question Video: Determining the Equation That Represents a Straight Line Mathematics • 9th Grade

Which of the following equations represents a straight line? [A] π¦ = β(π₯) + 6 [B] π¦ + (1/π₯) = β8 [C] π₯ + β(π¦) = β5 [D] β7π₯ β 2π¦ = β9

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### 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 weβre gonna do is look at a couple of the general forms for the equation of a straight line. Well, the couple of forms that weβve got here are the standard form, π΄π₯ plus π΅π¦ equals πΆ, 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 thatβs 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, letβs 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 donβt have the π₯ to the power of one, π¦ to the power of one.

Then, if we take a look at (C), once again, weβve got a root, and this time itβs root π¦. So therefore, this is gonna be π¦ to the power of a half. So therefore, this canβt 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 πΆ. So therefore, we can say that the equation which represents the straight line is negative seven π₯ minus two π¦ equals negative nine. And itβs in the standard form π΄π₯ plus π΅π¦ equals πΆ, where π΄ is equal to negative seven, π΅ is equal to negative two, and πΆ is equal to negative nine. Okay, great, so weβve solved this problem.