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

Video Transcript

Which of the following equations represents a straight line? (A) 𝑦 equals root 𝑥 plus six, (B) 𝑦 plus one over 𝑥 equals negative eight, (C) 𝑥 plus root 𝑦 equals negative five, or (D) negative seven 𝑥 minus two 𝑦 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 we’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 we’ve got here are the standard form, 𝐴𝑥 plus 𝐵𝑦 equals 𝐶, or we have the point-slope form, which is 𝑦 minus 𝑦 sub one equals 𝑚 multiplied by 𝑥 minus 𝑥 sub one.

Well, one thing we can notice from both of our forms is the fact that we have here 𝑥 to the power of one and then 𝑦 to the power of one. And that’s in the standard form. And then in the point-slope form, we also have 𝑦 to the power of one or 𝑥 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, let’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 𝑥. Well, if we write this in exponent form, this is 𝑥 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 𝑥. Well, if we rewrite this in exponent form, this is 𝑥 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 don’t have the 𝑥 to the power of one, 𝑦 to the power of one.

Then, if we take a look at (C), once again, we’ve got a root, and this time it’s root 𝑦. So therefore, this is gonna be 𝑦 to the power of a half. So therefore, this can’t be the correct equation either.

But if we check equation (D), what we have here is 𝑥 to the power of one and 𝑦 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 𝐴𝑥 plus 𝐵𝑦 equals 𝐶. So therefore, we can say that the equation which represents the straight line is negative seven 𝑥 minus two 𝑦 equals negative nine. And it’s in the standard form 𝐴𝑥 plus 𝐵𝑦 equals 𝐶, where 𝐴 is equal to negative seven, 𝐵 is equal to negative two, and 𝐶 is equal to negative nine. Okay, great, so we’ve solved this problem.