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

Which of the following equations represents a straight line? [A] 𝑦 = √(π‘₯) + 6 [B] 𝑦 + (1/π‘₯) = βˆ’8 [C] π‘₯ + √(𝑦) = βˆ’5 [D] βˆ’7π‘₯ βˆ’ 2𝑦 = βˆ’9

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Video Transcript

Which of the following equations represents a straight line? (A) 𝑦 equals root π‘₯ plus six, (B) 𝑦 plus one over π‘₯ equals negative eight, (C) π‘₯ plus root 𝑦 equals negative five, or (D) negative seven π‘₯ 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, 𝐴π‘₯ plus 𝐡𝑦 equals 𝐢, or we have the point-slope form, which is 𝑦 minus 𝑦 sub one equals π‘š 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 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 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, 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 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 don’t have the π‘₯ 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 π‘₯ 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 𝐴π‘₯ plus 𝐡𝑦 equals 𝐢. So therefore, we can say that the equation which represents the straight line is negative seven π‘₯ minus two 𝑦 equals negative nine. And it’s in the standard form 𝐴π‘₯ plus 𝐡𝑦 equals 𝐢, where 𝐴 is equal to negative seven, 𝐡 is equal to negative two, and 𝐢 is equal to negative nine. Okay, great, so we’ve solved this problem.

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