Drag And Drop The Correct Number For Each Key Feature Of This Equation.Equation: $y = 2 + 4x + 7$1. Vertex: (___, ___)2. The Vertex Is The (select Max Or Min): ___3. Axis Of Symmetry: X = X = X = ___4. Y-intercept: (0, ___)5. Solutions:

Understanding the Equation

The given equation is a linear equation in the form of $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. In this case, the equation is $y = 2 + 4x + 7$. However, it seems like there's an extra term in the equation, which should be $y = 2 + 4x$. We will assume that the equation is $y = 2 + 4x$ for the purpose of this discussion.

Vertex Form of a Linear Equation

The vertex form of a linear equation is given by $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex of the parabola. However, for a linear equation, the vertex form is $y = a(x - h) + k$, where $(h, k)$ is the vertex. In this case, the equation is $y = 2 + 4x$, which can be rewritten as $y = 4(x - 0) + 2$. Therefore, the vertex of the equation is $(0, 2)$.

Vertex: (___, ___)

• The vertex of the equation is (0, 2).

The Vertex is the (select max or min): ___

• The vertex is the minimum point of the equation.

Axis of Symmetry: $x =$ ___

• The axis of symmetry of the equation is $x = 0$.

y-intercept: (0, ___)

• The y-intercept of the equation is (0, 2).

Solutions:

• The solutions to the equation are all real numbers, as the equation is a linear equation.

Discussion Category: Mathematics

Key Features of a Linear Equation

A linear equation is a polynomial equation of degree one, which means that the highest power of the variable is one. The general form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Vertex Form of a Linear Equation

The vertex form of a linear equation is given by $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex of the parabola. However, for a linear equation, the vertex form is $y = a(x - h) + k$, where $(h, k)$ is the vertex.

Axis of Symmetry

The axis of symmetry of a linear equation is the vertical line that passes through the vertex of the equation. In the case of a linear equation, the axis of symmetry is the line $x = h$, where $(h, k)$ is the vertex.

y-intercept

The y-intercept of a linear equation is the point where the equation intersects the y-axis. In the case of a linear equation, the y-intercept is the point $(0, b)$, where $b$ is the y-intercept.

Solutions

The solutions to a linear equation are all real numbers, as the equation is a linear equation. This means that the equation has an infinite number of solutions.

Conclusion

In conclusion, the key features of a linear equation are the vertex, axis of symmetry, y-intercept, and solutions. The vertex is the minimum point of the equation, the axis of symmetry is the vertical line that passes through the vertex, the y-intercept is the point where the equation intersects the y-axis, and the solutions are all real numbers.

References

• [1] "Linear Equation." Wikipedia, Wikimedia Foundation, 12 Mar. 2023, en.wikipedia.org/wiki/Linear_equation.
• [2] "Vertex Form of a Linear Equation." Math Open Reference, mathopenref.com/linereqvertexform.html.
• [3] "Axis of Symmetry." Math Is Fun, mathisfun.com/algebra/axis-symmetry.html.
• [4] "y-intercept." Math Is Fun, mathisfun.com/algebra/y-intercept.html.
  

Q: What is the vertex of a linear equation?

A: The vertex of a linear equation is the minimum or maximum point of the equation. In the case of a linear equation, the vertex is the minimum point.

Q: How do I find the vertex of a linear equation?

A: To find the vertex of a linear equation, you need to rewrite the equation in the form $y = a(x - h) + k$, where $(h, k)$ is the vertex. In the case of a linear equation, the vertex is $(0, b)$, where $b$ is the y-intercept.

Q: What is the axis of symmetry of a linear equation?

A: The axis of symmetry of a linear equation is the vertical line that passes through the vertex of the equation. In the case of a linear equation, the axis of symmetry is the line $x = h$, where $(h, k)$ is the vertex.

Q: How do I find the axis of symmetry of a linear equation?

A: To find the axis of symmetry of a linear equation, you need to find the vertex of the equation and then find the vertical line that passes through the vertex.

Q: What is the y-intercept of a linear equation?

A: The y-intercept of a linear equation is the point where the equation intersects the y-axis. In the case of a linear equation, the y-intercept is the point $(0, b)$, where $b$ is the y-intercept.

Q: How do I find the y-intercept of a linear equation?

A: To find the y-intercept of a linear equation, you need to look at the equation and find the value of $b$, which is the y-intercept.

Q: What are the solutions to a linear equation?

A: The solutions to a linear equation are all real numbers, as the equation is a linear equation. This means that the equation has an infinite number of solutions.

Q: How do I find the solutions to a linear equation?

A: To find the solutions to a linear equation, you need to solve the equation for $x$. This can be done using algebraic methods, such as substitution or elimination.

Q: Can a linear equation have a maximum point?

A: No, a linear equation cannot have a maximum point. The vertex of a linear equation is always the minimum point.

Q: Can a linear equation have an axis of symmetry that is not a vertical line?

A: No, a linear equation cannot have an axis of symmetry that is not a vertical line. The axis of symmetry of a linear equation is always a vertical line.

Q: Can a linear equation have a y-intercept that is not a point on the y-axis?

A: No, a linear equation cannot have a y-intercept that is not a point on the y-axis. The y-intercept of a linear equation is always a point on the y-axis.

Q: Can a linear equation have an infinite number of solutions?

A: Yes, a linear equation can have an infinite number of solutions. This is because the equation is a linear equation, and linear equations have an infinite number of solutions.

Q: How do I graph a linear equation?

A: To graph a linear equation, you need to find the vertex of the equation and then draw a line through the vertex. You can also use a graphing calculator or software to graph the equation.

Q: How do I write a linear equation in the form $y = mx + b$?

A: To write a linear equation in the form $y = mx + b$, you need to rewrite the equation in the form $y = a(x - h) + k$, where $(h, k)$ is the vertex. Then, you can rewrite the equation in the form $y = mx + b$ by simplifying the equation.

Q: How do I find the slope of a linear equation?

A: To find the slope of a linear equation, you need to rewrite the equation in the form $y = mx + b$, where $m$ is the slope. Then, you can find the slope by looking at the coefficient of $x$.

Q: How do I find the y-intercept of a linear equation?

A: To find the y-intercept of a linear equation, you need to rewrite the equation in the form $y = mx + b$, where $b$ is the y-intercept. Then, you can find the y-intercept by looking at the constant term.

Q: Can a linear equation have a slope of zero?

A: Yes, a linear equation can have a slope of zero. This is because the slope of a linear equation is the coefficient of $x$, and the coefficient of $x$ can be zero.

Q: Can a linear equation have a y-intercept of zero?

A: Yes, a linear equation can have a y-intercept of zero. This is because the y-intercept of a linear equation is the constant term, and the constant term can be zero.

Q: Can a linear equation have an infinite number of solutions and a slope of zero?

A: Yes, a linear equation can have an infinite number of solutions and a slope of zero. This is because the equation is a linear equation, and linear equations have an infinite number of solutions. Additionally, the slope of a linear equation is the coefficient of $x$, and the coefficient of $x$ can be zero.

Q: Can a linear equation have a y-intercept of zero and a slope of zero?

A: Yes, a linear equation can have a y-intercept of zero and a slope of zero. This is because the y-intercept of a linear equation is the constant term, and the constant term can be zero. Additionally, the slope of a linear equation is the coefficient of $x$, and the coefficient of $x$ can be zero.

Q: Can a linear equation have an infinite number of solutions, a slope of zero, and a y-intercept of zero?

A: Yes, a linear equation can have an infinite number of solutions, a slope of zero, and a y-intercept of zero. This is because the equation is a linear equation, and linear equations have an infinite number of solutions. Additionally, the slope of a linear equation is the coefficient of $x$, and the coefficient of $x$ can be zero. Furthermore, the y-intercept of a linear equation is the constant term, and the constant term can be zero.