For each equation, (a) give a table with at least three ordere...

Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. 2x+3y=5

Accepted Answer

Hello everybody. I hope we're doing. All right. Today, today we're gonna be looking at this math question that says for the following equation, identify three ordered pairs and show that the graph passes through these points. And now the equation given is seven X plus 21 Y equals 42. Now, the extras provided are a, a line angled downwards passing through the 0.0 comma 36 comma zero and 15 comma negative nine halves. As choice B is a line angled downwards passing through the 0.0. Comma 3/2 divided by 26 comma negative three divided by two and 15 comma negative six A is a line angled upwards passing through the 0.0 comma negative 36 comma zero and 15 comma nine halves and answer choice CD is a line angle downwards passing through the points zero, comma two and six comma zero. So the first one I wanna do when looking at this equation, we can see that this is kind of a line equation. We have X values and Y values. So the first thing we can do is check for X intercepts and Y intercepts. So to do that we have to plug in zero for each one of the variables to find the other one. So when we have an X intercept, we know that Y is equal to zero. So at Y equals zero, we would have seven X plus multiplied by zero, equal to 42. We know that 21 multiplied by zero will be zero. So we're left with the seven X is equal to 42. And then we just have to simplify now divide both sides by seven. And we would have that X is equal to six. So we have that the X intercept is equal to six comma zero. And now we look for the Y intercept, so the Y intercept would be at X equals zero. So we do the same thing we did, we plug instead, now we plug in zero for the X. So we do seven multiplied by zero. Now plus 21 Y is equal to 42 seven, multiplied by zero is zero. So we're left with 21 Y equals 42. And now once again, we just simplify, divide both sides by 21. So we'll have Y is equal to two. So the Y intercept is equal to zero comma two. So now let's check our graphs, our answer choices. See if anyone, any of them match up with this. We're looking at answer choice A, we see that the Y intercept is at zero comma three. The X intercept is correct. They have it at six common zero, but they have a different Y intercept. So we can eliminate that answer choice because it does not match with our graph. Now, we move on to answer choice. B they have a Y intercept of zero comma three halves and the X intercept is not given to us, but that Y intercept is already enough to eliminate this edge choice because it does not not match up with our graph. Now, we move on to a C, they have a Y intercept of zero comma negative three, which does not match with our graph. Their X intercept does, but it doesn't. But the Y intercept is enough to eliminate this. And now finally, we move on to as choice D and once again, I'll, I'll just write the X intercept just to remind us that it was six comma zero. And that's exactly what they have. They have a Y intercept of zero comma two and that's what we have. And then they have a X intercept of six comma zero. Now, they don't provide us any other points. But if we wanted to uh check any other points, all we would have to do is plug them into our, our equation. So once again, a reminder would be seven X plus 21 Y equals 42. If we wanted to check any other point along this line, then all we would have to do is plug those numbers into our equation. Let's say we wanted to test the point, let's say three comma five or something. You just plug in that the, whatever X value you want into that X and then whatever X value you want or Y value into that Y. And that would tell you if that point works. If you don't want to test a specific point, what you could do is just test and one of the, of the variables. So plug in an X value and see what the Y value would be. And then that would tell you where that line would intercept that point. But as we mentioned, since we were able to eliminate every other answer, N D has the same Y intercept and X intercept as we do, we can confidently say that D is the answer for this question. So I hope that was helpful. And until next time.

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. 2x+3y=5

Key Concepts

Solving Linear Equations for One Variable

Ordered Pairs as Solutions to Equations

Graphing Linear Equations

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