Question Video: Determining the Equation That Represents a Straight Line | Nagwa Question Video: Determining the Equation That Represents a Straight Line | Nagwa

Question Video: Determining the Equation That Represents a Straight Line Mathematics

Which of the following equations represents a straight line? [A] 𝑦 = √(𝑥) + 6 [B] 𝑦 + (1/𝑥) = −8 [C] 𝑥 + √(𝑦) = −5 [D] −7𝑥 − 2𝑦 = −9

02:33

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.

Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

  • Interactive Sessions
  • Chat & Messaging
  • Realistic Exam Questions

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy