Make Sense? In Exercises 67–70, determine whether each statement ...

Question

Make Sense? In Exercises 67–70, determine whether each statement makes sense or does not make sense, and explain your reasoning.

I used the ordered pairs (- 2, 2), (0, 0), and (2, 2) to graph a straight line.

Accepted Answer

Welcome back. I'm so glad you're here. We're being asked whether or not we can graph a straight line using these three ordered pairs. And if we can't to explain why not. So I am going to draw a very rough sketch of a graph and point out a few things so that we can figure out if we can in fact draw a straight line with these three ordered pairs. So with a graph we have a horizontal X axis and a vertical Y axis where they come together that's called the origin and the Y values. As you go up in your units we are gaining positive numbers and as you go down in your units we have negative numbers and those will typically be labeled so that you know the scale. So if the first one is one and the next one would be two and so on. And then going down you'd have a negative one, negative two negative three and so on. And then X values work much the same way going to the right they are positive and they will give you values to indicate you're going 123 and so on and going to the left they will be negative. So you will have it marked negative one negative two negative three and so on. And when you have an ordered pair that is always going to give you your X value first followed by your y value. So that's a lot of information so that we can begin to graph these three ordered pairs. Let's take a look at the first one here 1 1 the X value comes first so that's one on the X axis. So we go one to the right of the origin and then our Y. Value is also one. That means we're going to go from that X value. We're going to go up one so that we're at one for the X. Value and one for the Y. Value. And that's where that one is plotted. This second ordered pair here we have one for the X. Value and two for the Y value. So we go to the right one for X. And we go up to for Y. And we are located right above the previous dot and hey this is looking good so far this looks like it could be a straight line. Let's draw our last one. Now we have two for the X. Value and one for the Y. Value. So we go to the right to for our X. Value and up one for our Y. Value. But now no we could not possibly draw a straight line between those three points. So we know it's not going to be a now we want to look at why it could be false. Let's look at d false because the order pairs are too close together and thus impossible to graph. Well I mean if that's your problem you can always scale your graph differently so that's not going to be a reason why you couldn't graph something you can just zoom in or zoom out if you needed to see false because the ordered pairs when trace former parabola. Well no, not necessarily. This um doesn't look like a parabola here. And so that is not the reason why we can't form a single line. So we land on be false because the ordered pairs when plotted cannot coexist on one single line. And that's true. So we go with answer choice B. Well done, we'll catch you on the next one.

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