If Y = − 5 + 2 X Y = -5 + 2x Y = − 5 + 2 X , Then What Are The Corresponding Y Y Y Values For X = 1 , 2 , 3 X = 1, 2, 3 X = 1 , 2 , 3 ?A. 1, 2, 3 B. 5 , 9 , 11 5, 9, 11 5 , 9 , 11 C. − 5 , − 1 , 1 -5, -1, 1 − 5 , − 1 , 1 D. − 3 , − 1 , 1 -3, -1, 1 − 3 , − 1 , 1 E. − 5 , − 10 , − 15 -5, -10, -15 − 5 , − 10 , − 15

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Introduction

In mathematics, linear equations are a fundamental concept that helps us understand the relationship between variables. A linear equation is an equation in which the highest power of the variable(s) is 1. In this article, we will focus on solving linear equations of the form y = mx + b, where m is the slope and b is the y-intercept. We will use the given equation y = -5 + 2x to find the corresponding y values for x = 1, 2, 3.

Understanding the Equation

The given equation is y = -5 + 2x. This equation represents a linear relationship between the variables x and y. The slope of the equation is 2, which means that for every unit increase in x, y increases by 2 units. The y-intercept is -5, which means that when x is 0, y is -5.

Finding Corresponding y Values

To find the corresponding y values for x = 1, 2, 3, we will substitute these values into the equation y = -5 + 2x.

For x = 1

Substituting x = 1 into the equation, we get:

y = -5 + 2(1) y = -5 + 2 y = -3

So, the corresponding y value for x = 1 is -3.

For x = 2

Substituting x = 2 into the equation, we get:

y = -5 + 2(2) y = -5 + 4 y = -1

So, the corresponding y value for x = 2 is -1.

For x = 3

Substituting x = 3 into the equation, we get:

y = -5 + 2(3) y = -5 + 6 y = 1

So, the corresponding y value for x = 3 is 1.

Conclusion

In this article, we used the equation y = -5 + 2x to find the corresponding y values for x = 1, 2, 3. We substituted these values into the equation and solved for y. The corresponding y values are -3, -1, and 1, respectively.

Answer

The correct answer is D. -3, -1, 1.

Tips and Tricks

  • When solving linear equations, make sure to substitute the given values into the equation correctly.
  • Use the slope and y-intercept to understand the relationship between the variables.
  • Practice solving linear equations to become more comfortable with the concept.

Real-World Applications

Linear equations have many real-world applications, such as:

  • Modeling population growth
  • Calculating the cost of goods
  • Determining the trajectory of an object
  • Understanding the relationship between variables in a system

Common Mistakes

  • Failing to substitute the given values into the equation correctly
  • Not using the slope and y-intercept to understand the relationship between the variables
  • Not practicing solving linear equations to become more comfortable with the concept

Conclusion

Introduction

In our previous article, we discussed how to solve linear equations of the form y = mx + b. We used the equation y = -5 + 2x to find the corresponding y values for x = 1, 2, 3. In this article, we will answer some frequently asked questions about solving linear equations.

Q&A

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(s) is 1. A quadratic equation, on the other hand, is an equation in which the highest power of the variable(s) is 2. For example, y = 2x + 3 is a linear equation, while y = x^2 + 2x + 1 is a quadratic equation.

Q: How do I know if an equation is linear or quadratic?

A: To determine if an equation is linear or quadratic, look at the highest power of the variable(s). If the highest power is 1, the equation is linear. If the highest power is 2, the equation is quadratic.

Q: What is the slope of a linear equation?

A: The slope of a linear equation is the coefficient of the variable. In the equation y = mx + b, the slope is m. The slope represents the rate of change of the variable.

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

A: To find the y-intercept of a linear equation, set the variable equal to 0 and solve for y. In the equation y = mx + b, the y-intercept is b.

Q: Can I solve a linear equation with fractions?

A: Yes, you can solve a linear equation with fractions. To do this, multiply both sides of the equation by the least common multiple (LCM) of the denominators.

Q: How do I solve a linear equation with decimals?

A: To solve a linear equation with decimals, follow the same steps as solving a linear equation with fractions. Multiply both sides of the equation by the LCM of the denominators.

Q: Can I solve a linear equation with negative numbers?

A: Yes, you can solve a linear equation with negative numbers. To do this, follow the same steps as solving a linear equation with positive numbers.

Q: How do I graph a linear equation?

A: To graph a linear equation, use the slope-intercept form (y = mx + b). Plot the y-intercept (b) on the y-axis, and then use the slope (m) to find the next point on the line.

Q: Can I solve a linear equation with variables on both sides?

A: Yes, you can solve a linear equation with variables on both sides. To do this, add or subtract the same value to both sides of the equation to isolate the variable.

Tips and Tricks

  • When solving linear equations, make sure to follow the order of operations (PEMDAS).
  • Use the slope and y-intercept to understand the relationship between the variables.
  • Practice solving linear equations to become more comfortable with the concept.

Real-World Applications

Linear equations have many real-world applications, such as:

  • Modeling population growth
  • Calculating the cost of goods
  • Determining the trajectory of an object
  • Understanding the relationship between variables in a system

Common Mistakes

  • Failing to follow the order of operations (PEMDAS)
  • Not using the slope and y-intercept to understand the relationship between the variables
  • Not practicing solving linear equations to become more comfortable with the concept

Conclusion

In conclusion, solving linear equations is an essential concept in mathematics. By understanding the equation y = -5 + 2x and substituting the given values into the equation, we can find the corresponding y values for x = 1, 2, 3. We also answered some frequently asked questions about solving linear equations.