Solved on Feb 14, 2024

Determine why the equation $y=-x^{2}+1$ does not represent a line.

STEP 1

Assumptions
1. We are given the equation $y = -x^2 + 1$ .
2. We need to determine why this equation does not represent a line.

STEP 2

Recall the general form of the equation of a line, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 3

Compare the given equation $y = -x^2 + 1$ with the general form of a line.

STEP 4

Identify that the term $-x^2$ indicates that $x$ is raised to the second power, which is not a characteristic of a linear equation.

STEP 5

Recognize that the presence of an $x^2$ term means the equation represents a parabola, not a line.

STEP 6

Conclude that option A, " $x$ is squared," is the correct reason why the equation $y = -x^2 + 1$ does not represent a line.
The correct answer is A, because the presence of an $x^2$ term indicates that the graph of the equation is a parabola, which is a curve, not a straight line.

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Determine why the equation $y=-x^{2}+1$ does not represent a line.

STEP 1

Assumptions
1. We are given the equation $y = -x^2 + 1$ .
2. We need to determine why this equation does not represent a line.

STEP 2

Recall the general form of the equation of a line, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 3

Compare the given equation $y = -x^2 + 1$ with the general form of a line.

STEP 4

Identify that the term $-x^2$ indicates that $x$ is raised to the second power, which is not a characteristic of a linear equation.

STEP 5

Recognize that the presence of an $x^2$ term means the equation represents a parabola, not a line.

STEP 6

Conclude that option A, " $x$ is squared," is the correct reason why the equation $y = -x^2 + 1$ does not represent a line.
The correct answer is A, because the presence of an $x^2$ term indicates that the graph of the equation is a parabola, which is a curve, not a straight line.

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Determine why the equation y=−x2+1y=-x^{2}+1y=−x2+1 does not represent a line.

STEP 1

Assumptions1. We are given the equation y=−x2+1y = -x^2 + 1y=−x2+1.2. We need to determine why this equation does not represent a line.

STEP 2

Recall the general form of the equation of a line, which is y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.

STEP 3

Compare the given equation y=−x2+1y = -x^2 + 1y=−x2+1 with the general form of a line.

STEP 4

Identify that the term −x2-x^2−x2 indicates that xxx is raised to the second power, which is not a characteristic of a linear equation.

STEP 5

Recognize that the presence of an x2x^2x2 term means the equation represents a parabola, not a line.

STEP 6

Conclude that option A, "xxx is squared," is the correct reason why the equation y=−x2+1y = -x^2 + 1y=−x2+1 does not represent a line.The correct answer is A, because the presence of an x2x^2x2 term indicates that the graph of the equation is a parabola, which is a curve, not a straight line.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Determine why the equation $y=-x^{2}+1$ does not represent a line.

Assumptions
1. We are given the equation $y = -x^2 + 1$ .
2. We need to determine why this equation does not represent a line.

Recall the general form of the equation of a line, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

Compare the given equation $y = -x^2 + 1$ with the general form of a line.

Identify that the term $-x^2$ indicates that $x$ is raised to the second power, which is not a characteristic of a linear equation.

Recognize that the presence of an $x^2$ term means the equation represents a parabola, not a line.

Conclude that option A, " $x$ is squared," is the correct reason why the equation $y = -x^2 + 1$ does not represent a line.
The correct answer is A, because the presence of an $x^2$ term indicates that the graph of the equation is a parabola, which is a curve, not a straight line.