Find the slope and y-intercept of each line, and graph it. 4x-...

Question

Find the slope and y-intercept of each line, and graph it. 4x-y =7

Accepted Answer

Hello everybody. I hope you're doing right today. Today we're gonna be looking at this math question that's telling us to determine the Y intercept and the slope of the line defined by the following equation then graph the line. Now the equation that they give us is two X plus three, Y is equal to negative 17. And the S provided are a, a graph with the slope of negative two thirds and A Y intercept of negative 17 3rd passing through the points, negative 17 halves, comma zero and zero. Comma negative 17 3rd. B is a graph with a slope of two thirds positive two thirds and A Y. And the same Y intercept as a passing through the points is zero, comma negative 17 3rd and 17 halves comma zero. Answer choice C is a graph with a slope of negative two thirds and A Y intercept of positive 17 3rd passing through the points zero, comma 17 3rd and 17 halves comma zero. And as choice D is a graph with a slope of positive two thirds. And the same lines are set to C passing through the points negative 17 halves, comma zero and zero comma 17 3rd. No, the first thing we can do when looking at this equation is see how we can manipulate this into something that can help us a little more. Now, this has a Y and an X equal to a number. So this can be rearranged into Y equals M X plus B, which is the line equation where M equals slope and B equals Y intercept. So let's rearrange this to get exactly that. Now, we once again, we had two X plus three, Y equals negative 17. So let's move the two X over from the left hand side of the equation to the right hand side. And we'll have three Y, it's equal to negative two X minus 17. And now we can divide both sides by three to isolate the Y and we'll have Y is equal to negative two thirds, X minus 17 3rd. And that's gonna match our Y equals M X plus B equation. So we can work from there where are slow is negative two thirds and are Y intercept is negative 17 3rd or zero comma negative 3rd. So let's look for that. Let's, let's look at our s choices. A choice A has a slope of negative two thirds, which is what we have and a set of negative 17 3rd, which is also what we have. Answer. Choice B has a slope of positive two thirds which is not what we have. So we can eliminate it. A choice C has the same slope that we have negative two thirds, but a different one intercept positive 17 3rd. So we eliminate aster choice C A, a choice C has a slope of positive two thirds, which is not what we have. So we can eliminate a choice B as well. And with that, we can now focus on answer choice A. So now all we have to do is plug in the other point that they gave us because they gave us the Y intercept, which is zero, comma negative 17 3rd. And the other point that they gave us was negative 17 halves, comma zero. So let's test that point, see if it matches and fits our equation. Now, remember we had Y is equal to negative two thirds, X minus 17 3rd. So we plug in zero for Y because that's the point that they gave us. So one plug in 04 Y and that'll be equal to negative two thirds multiplied by X minus 17 3rd. So we can move that negative 17 3rd over from the right hand side to the left hand side. And we'll have positives 17 3rd is equal to negative two thirds multiplied by X. And now we divide both sides by negative two thirds. So we'll have 17 3rd divided by negative two thirds on the left hand side. And that'll be equal to X. And this is the same thing as saying 17 3rd multiplied by negative three halves and they'll be equal to X. And now the threes will cancel because you have 17 3rd multiplied by negative three halves. So since you have three in the denominator on one side and three in the numerator on the other side, they will cancel. And we're gonna be left with negative 17 halves equal to X or the point, negative 17 halves, comma zero which matches the point in the graph and confirms that answer choice. A is the correct answer for this question. So I hope that was helpful and until next time.

Find the slope and y-intercept of each line, and graph it. 4x-y =7

Key Concepts

Slope-Intercept Form of a Line

Slope of a Line

Y-Intercept of a Line

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