For The Equation $y = -2x - 2$, Calculate The Following $y$ Values:- When $x = -2$, $y = \square$- When $x = 1$, $y = \square$Now, Graph The Equation And Answer The Following Questions:- Is $(0,

Introduction

In this article, we will be solving a linear equation and graphing it to understand its behavior. The equation given is $y = -2x - 2$. We will first calculate the $y$ values for specific $x$ values and then graph the equation to visualize its behavior.

Calculating y Values

To calculate the $y$ values, we will substitute the given $x$ values into the equation $y = -2x - 2$.

When $x = -2$

When $x = -2$, we substitute this value into the equation:

$$y = -2(-2) - 2$$

Simplifying the equation, we get:

$$y = 4 - 2$$

$$y = 2$$

So, when $x = -2$, $y = 2$.

When $x = 1$

When $x = 1$, we substitute this value into the equation:

$$y = -2(1) - 2$$

Simplifying the equation, we get:

$$y = -2 - 2$$

$$y = -4$$

So, when $x = 1$, $y = -4$.

Graphing the Equation

To graph the equation, we can use the two points we calculated earlier: $( -2, 2)$ and $(1, -4)$. We can plot these points on a coordinate plane and draw a line through them to represent the equation.

Graph

Here is a graph of the equation $y = -2x - 2$:

  +---------------------------------------+
  |                                             |
  |  +---------------------------------------+
  |  |  (0, 0)                                |
  |  |  +---------------------------------------+
  |  |  |  ( -2, 2)                            |
  |  |  |  (1, -4)                             |
  |  |  +---------------------------------------+
  |  |                                             |
  |  +---------------------------------------+
  |                                             |
  +---------------------------------------+

Discussion Questions

Now that we have graphed the equation, let's answer some discussion questions:

Is $(0, 0)$ a solution to the equation?

To determine if $(0, 0)$ is a solution to the equation, we can substitute $x = 0$ and $y = 0$ into the equation:

$$0 = -2(0) - 2$$

Simplifying the equation, we get:

$$0 = -2$$

This is not true, so $(0, 0)$ is not a solution to the equation.

Is the graph of the equation a function?

To determine if the graph of the equation is a function, we need to check if each $x$ value corresponds to only one $y$ value. In this case, we can see that each $x$ value corresponds to only one $y$ value, so the graph of the equation is a function.

What is the domain of the equation?

The domain of the equation is all real numbers, since there are no restrictions on the values of $x$.

What is the range of the equation?

The range of the equation is all real numbers less than or equal to $-2$, since the lowest value of $y$ is $-2$.

Conclusion

$$$$

Introduction

In our previous article, we solved a linear equation and graphed it to understand its behavior. We calculated the $y$ values for specific $x$ values and then graphed the equation to visualize its behavior. In this article, we will answer some frequently asked questions about solving linear equations and graphing.

Q&A

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (usually $x$) is 1. In other words, it is an equation that can be written in the form $y = mx + b$, where $m$ and $b$ are constants.

Q: How do I solve a linear equation?

A: To solve a linear equation, you can use the following steps:

1. Simplify the equation by combining like terms.
2. Isolate the variable (usually $x$) by adding or subtracting the same value to both sides of the equation.
3. Divide both sides of the equation by the coefficient of the variable (usually $x$).

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable (usually $x$) is 1, while a quadratic equation is an equation in which the highest power of the variable (usually $x$) is 2. In other words, a linear equation can be written in the form $y = mx + b$, while a quadratic equation can be written in the form $y = ax^2 + bx + c$.

Q: How do I graph a linear equation?

A: To graph a linear equation, you can use the following steps:

1. Find two points on the graph by substituting different values of $x$ into the equation.
2. Plot the points on a coordinate plane.
3. Draw a line through the points to represent the equation.

Q: What is the domain of a linear equation?

A: The domain of a linear equation is all real numbers, since there are no restrictions on the values of $x$.

Q: What is the range of a linear equation?

A: The range of a linear equation is all real numbers, since the lowest value of $y$ is $-\infty$ and the highest value of $y$ is $\infty$.

Q: Can a linear equation have a negative slope?

A: Yes, a linear equation can have a negative slope. In fact, the slope of a linear equation is determined by the coefficient of the variable (usually $x$).

Q: Can a linear equation have a zero slope?

A: Yes, a linear equation can have a zero slope. This occurs when the coefficient of the variable (usually $x$) is zero.

Q: Can a linear equation have a fractional slope?

A: Yes, a linear equation can have a fractional slope. This occurs when the coefficient of the variable (usually $x$) is a fraction.

Q: Can a linear equation have a negative y-intercept?

A: Yes, a linear equation can have a negative y-intercept. This occurs when the constant term (usually $b$) is negative.

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

A: Yes, a linear equation can have a zero y-intercept. This occurs when the constant term (usually $b$) is zero.

Conclusion

In this article, we answered some frequently asked questions about solving linear equations and graphing. We covered topics such as the definition of a linear equation, how to solve a linear equation, the difference between a linear equation and a quadratic equation, and how to graph a linear equation. We also covered topics such as the domain and range of a linear equation, and whether a linear equation can have a negative slope, zero slope, fractional slope, negative y-intercept, or zero y-intercept.