Video: SAT Practice Test 1 β€’ Section 3 β€’ Question 9

A line in the π‘₯𝑦-plane has a slope of 8 and passes through the origin. Which of the following is a point on the line? [A] (1/8, 1) [B] (2, 1/4) [C] (1/4, 1) [D] (1, 1/8)

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Video Transcript

A line in the π‘₯𝑦-plane has a slope of eight and passes through the origin. Which of the following is a point on the line? A) One-eighth, one; B) two, one-fourth; C) one-fourth, one; or D) one, one-eighth.

So in order to decide which of these points lies on our line, we first need to find the equation of our line. The equation of a line is 𝑦 equals π‘šπ‘₯ plus 𝑏, where π‘š is the slope and 𝑏 is the 𝑦-intercept. We are given that the slope is eight. So we know that the slope is eight. But what about 𝑏, the 𝑦-intercept?

Well, we’re told that this line passes through the origin. So on an π‘₯𝑦-plane, the origin is located here, at the point zero, zero. And the 𝑦-intercept is where this line will cross the 𝑦-axis. Well, here’s the 𝑦-axis. And we know where it’s actually gonna cross the 𝑦-axis. It’ll cross the 𝑦-axis at zero, zero. So the value of 𝑦 would be zero. So we could plug in zero for our 𝑦-intercept. So we would have the equation of a line as 𝑦 equals eight π‘₯ plus zero, which we don’t have to include the plus zero. We could just write 𝑦 equals eight π‘₯.

Another way that we could’ve got in our equation of the line would be we could plug in eight for π‘š and then zero for π‘₯ and zero for 𝑦 and then solve for 𝑏, the 𝑦-intercept. So we would have zero equals eight times zero plus 𝑏. And eight times zero is zero. And then 𝑏 plus zero gives us that 𝑏 is equal to zero, which we’ve already found here.

But as we said in the beginning, knowing that this line passes through the origin, it’s intuitive to know that the 𝑦-intercept indeed would just be zero. So now let’s go through each of these points, plug them into our equation, and see if they satisfy the equation. So we need to take each of our points and plug them into our equation: 𝑦 equals eight π‘₯ plus zero. And again, we can just use 𝑦 equals eight π‘₯. There’s no need to put plus zero.

So, so far, we’ve plugged in all of the 𝑦-values. And then we put equals eight times all of the π‘₯-values. And now we’ve done so. So let’s begin with option A). We have one equals eight times one-eighth. Well, the eights cancel, and we’re left with one. So one equals one. This satisfies the equation of the line. So that means the line passes through this point. But let’s go ahead and check all of the other options to be sure.

For option B), we have one-fourth equals eight times two. Well, eight times two is 16. And one-fourth is not equal to 16. So point B), option B), the line does not pass through this point.

For option C), we get one equals two because four goes into eight twice, and two times one is two. One is not equal to two. So this is not our answer.

And then, lastly, for option D), eight times one is eight. And one-eighth is not equal to eight. So D) is not our answer either.

So as we said before, option A) will be the correct answer. The point that is actually on this line would be one-eighth, one.

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