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. y=(1/2)x-2

Accepted Answer

Hello everybody. I hope we're doing. All right today today today we're gonna be looking at this math question that's telling us for the following equation identify three ordered pairs and show that the graph passes through these pairs, these points. So the equation that they give us is why equals one divided by seven, multiplied by X minus one. And the answers or choices that they provide us are a aligned with the positive slope passing through the points, negative seven comma negative 20, comma negative one and seven comma zero B aligned with a positive slope passing through the points, negative 14 comma negative 40, comma negative two and 14 comma zero C aligned with the positive slope passing through the points negative one comma negative 0 comma negative seven and one comma zero N D aligned with a positive slope passing through the points negative seven comma negative 14 0 comma negative seven and seven comma zero. So let's look back at our equation and we see that this matches the general line equation of Y equals M X plus B. This means that one divided by seven is a slope and our Y intercept is negative one. So let's just write that why intercept is negative one or the point is zero, comma negative one. So now let's try to software X intercept or X intercept occurs when why is equal to zero? So that's exactly what we do. We set our Y equals to zero and solve for that. So if we have zero is equal to one divided by seven, multiplied by X minus one. Now all we have to do is solve for X. So to do that, we move that one over from the right hand side to the left hand side. So we'll have positive one equals one divided by seven multiplied by X, which is the same as saying one is equal to X divided by seven. So we can move that seven over to the left hand side by multiplying by seven. So we would have that seven is equal to X or the X intercept is equal to the point seven comma zero. So now we have our Y intercept and our X intercept and right away by looking at answer choice A, we have that those two intercepts match. So we have the Y intercept of zero comma negative one checks out and the X intercept seven comma zero, which checks out now to check their last point, see if it matches our line as well. All we have to do is plug it in. So let's just plug in the X. So let's say uh X equals negative seven. We'll see if that gives us the same Y that they have in their point which is negative two. So we'll have Y is equal to one divided by seven. And now we're plugging in negative seven for the X and all that minus one. So we'll have Y equals one divided by seven, multiplied by negative seven minus one. So one divided by seven, multiplied by negative seven would just be negative one because the sevens will cancel out. So we'll have Y is equal to negative one minus one or Y is equal to negative two, which will give us the point negative seven comma negative two because we plugged in negative seven for our X and we got negative two as our Y which matches the point that they gave us in answer cha choice A as well. And with that, we can confirm that all three points match up with this graph, which means that this is our graph. So we can confidently say that answer choice A is the answer to 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. y=(1/2)x-2

Key Concepts

Slope-Intercept Form of a Linear Equation

Finding Ordered Pairs (Solutions) for a Linear Equation

Graphing Linear Equations

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