Consider The Equation: \[$-x - Y = 6\$\].a. Write The Equation In Slope-intercept Form.b. What Is The Slope Of The Line?c. What Is The \[$y\$\]-intercept Of The Line?

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Understanding the Equation

The given equation is −x−y=6{-x - y = 6}. This is a linear equation in two variables, x and y. To solve this equation, we need to isolate one of the variables.

Step 1: Write the Equation in Slope-Intercept Form

The slope-intercept form of a linear equation is y=mx+b{y = mx + b}, where m is the slope and b is the y-intercept. To write the given equation in slope-intercept form, we need to isolate y.

Step 1.1: Add x to both sides of the equation

−x−y=6{-x - y = 6} −y=6+x{-y = 6 + x}

Step 1.2: Multiply both sides of the equation by -1

y=−6−x{y = -6 - x}

The equation is now in slope-intercept form: y=−x−6{y = -x - 6}

Step 2: Find the Slope of the Line

The slope of a line is the coefficient of the x-term in the slope-intercept form of the equation. In this case, the slope is -1.

The slope of the line is −1{-1}

Step 3: Find the y-Intercept of the Line

The y-intercept of a line is the constant term in the slope-intercept form of the equation. In this case, the y-intercept is -6.

The y-intercept of the line is −6{-6}

Conclusion

In this article, we have solved the linear equation −x−y=6{-x - y = 6} and written it in slope-intercept form. We have also found the slope and y-intercept of the line. The slope of the line is -1, and the y-intercept is -6.

Key Takeaways

  • To write a linear equation in slope-intercept form, we need to isolate y.
  • The slope of a line is the coefficient of the x-term in the slope-intercept form of the equation.
  • The y-intercept of a line is the constant term in the slope-intercept form of the equation.

Frequently Asked Questions

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

A: The slope-intercept form of a linear equation is y=mx+b{y = mx + b}, where m is the slope and b is the y-intercept.

Q: How do I find the slope of a line?

A: To find the slope of a line, you need to look at the coefficient of the x-term in the slope-intercept form of the equation.

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

A: To find the y-intercept of a line, you need to look at the constant term in the slope-intercept form of the equation.

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Additional Resources

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form ax+by=c{ax + by = c}, where a, b, and c are constants, and x and y are variables.

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

A: The slope-intercept form of a linear equation is y=mx+b{y = mx + b}, where m is the slope and b is the y-intercept.

Q: How do I write a linear equation in slope-intercept form?

A: To write a linear equation in slope-intercept form, you need to isolate y. This can be done by adding or subtracting the same value from both sides of the equation, or by multiplying or dividing both sides of the equation by the same non-zero value.

Q: What is the slope of a line?

A: The slope of a line is the coefficient of the x-term in the slope-intercept form of the equation. In other words, it is the value that is multiplied by x.

Q: How do I find the slope of a line?

A: To find the slope of a line, you need to look at the coefficient of the x-term in the slope-intercept form of the equation.

Q: What is the y-intercept of a line?

A: The y-intercept of a line is the constant term in the slope-intercept form of the equation. In other words, it is the value that is added to the product of the slope and x.

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

A: To find the y-intercept of a line, you need to look at the constant term in the slope-intercept form of the equation.

Q: Can a linear equation have a slope of 0?

A: Yes, a linear equation can have a slope of 0. This occurs when the equation is in the form y=b{y = b}, where b is a constant.

Q: Can a linear equation have a y-intercept of 0?

A: Yes, a linear equation can have a y-intercept of 0. This occurs when the equation is in the form y=mx{y = mx}, where m is the slope.

Q: How do I graph a linear equation?

A: To graph a linear equation, you need to find two points on the line and draw a line through them. Alternatively, you can use the slope-intercept form of the equation to find the y-intercept and the slope, and then use a graphing calculator or software to graph the line.

Q: Can a linear equation have multiple solutions?

A: No, a linear equation can only have one solution. This is because a linear equation is a single equation, and it can only be true for one value of x and y.

Q: Can a linear equation have no solutions?

A: Yes, a linear equation can have no solutions. This occurs when the equation is inconsistent, meaning that it is impossible for the equation to be true for any value of x and y.

Q: How do I determine if a linear equation is consistent or inconsistent?

A: To determine if a linear equation is consistent or inconsistent, you need to check if the equation has a solution. If the equation has a solution, then it is consistent. If the equation does not have a solution, then it is inconsistent.

Q: Can a linear equation be used to model real-world situations?

A: Yes, a linear equation can be used to model real-world situations. For example, a linear equation can be used to model the cost of producing a certain number of items, or the distance traveled by an object.

Q: How do I use a linear equation to model a real-world situation?

A: To use a linear equation to model a real-world situation, you need to identify the variables and the relationships between them. You can then use the linear equation to make predictions or solve problems.

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