Which of the following could be the equation of the graph shown below

Video Transcript

graph shown below. So the first thing I'm gonna do is I'm gonna put this into slope intercept mode ah slope intercept form. So I have two x minus three, Y equals a negative nine. So I'm going to bring the two X over to the other side. So negative three Y equals negative two x -9. Then divide everything by a -3. So I get Y equals two thirds X plus three. So it can't be that one because it has a positive um Y intercept, it could be this one because it has a negative Y intercept and it has a positive slope. It cannot be this one because then the line would be horizontal. Um For the next one, Let's see. So four x plus two, Y equals a negative sex. So um If I move this four x over to the other side, It becomes negative. So two y equals negative four x -6. And then dividing by two. So I get Y equals a negative two x minus three. Now this is a negative slope. So it can't be that one because this is a positive slope. So the answer is B this is the middle school math teacher

Video Transcript

So in this problem, we want to they want us to determine which of the following. The functions could be the equation of the linear graph shown. So a says y equals negative two X plus five. So the y intercept is positive which is here and it has a negative slope which is also seen here. So that could be the line B. I'm gonna go ahead and get y by itself to see if that would work. So I'm gonna subtract acts to the other side, mm hmm. Then divide by -1. So that's why equals x minus nine. The y intercept is negative nine, which would not work for this graph. So that does not make sense for C. I'm gonna go ahead and get y by itself by subtracting two X. Yeah. So this has a y intercept of four, which could be the case here and a negative slope which is also seen in this graph. So, C could potentially work now, D would be a horizontal line at five, which is not seen here. So, the only answers here that could match that equation, R. A and C.

Which of the following could be the equation of the graph shown below? heck all that apply. A. 3x+2y=6 B. 2x-y=7 C. y=-4x+2 D. y=5

Question

Gauthmathier8630

Grade 8 · 2022-06-01

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Which of the following could be the equation of the graph shown below? heck all that apply.
A. Which of the following could be the equation of th - Gauthmath
B. 2x-y=7
C. y=-4x+2
D. y=5

Gauthmathier1851

Grade 8 · 2022-06-01

Answer

Explanation

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y = x(x − 2)(x + 3)`y = x^2(x − 2)(x + 3)`y = x(x + 2)(x − 3)`y = x^2(x + 2)(x − 3)`

Answer : B

Solution : The x-coordinates of the x-intercepts of the graph are –3, 0, and 2. This means that if y = f (x) is the equation of the graph, where f is a polynomial function, then (x + 3), x, and (x − 2) are factors of f. Of the choices given, A and B have the correct factors. However, in choice A, x is raised to the first power, and in choice B, x is raised to the second power. At x = 0, the graph touches the x-axis but doesn’t cross it. This means that x, as a factor of f, is raised to an even power. If x were raised to an odd power, then the graph would cross the x-axis. Alternatively, in choice A, f is a third-degree polynomial, and in choice B, f is a fourth-degree polynomial. The y-coordinates of points on the graph become large and positive as x becomes large and negative, this is consistent with a fourth-degree polynomial, but not with a third-degree polynomial. Therefore, of the choices given, only choice B could be the equation of the graph. Choice A is incorrect. The graph of the equation in this answer choice has the correct factors. However, at x = 0 the graph of the equation in this choice crosses the x-axis, the graph shown touches the x-axis but doesn’t cross it. Choices C and D are incorrect and are likely the result of misinterpreting the relationship between the x-intercepts of a graph of a polynomial function and the factors of the polynomial expression