Converting 4x 3y 9 To Slope Intercept Form Made Easy

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Converting an equation from standard form to slope-intercept form can be a daunting task for many students. However, with the right approach, it can be made easy and even enjoyable. In this article, we will explore how to convert the equation 4x + 3y = 9 to slope-intercept form.

Understanding the Standard Form of a Linear Equation

The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. In this form, the coefficients of x and y are written on the same side of the equation, and the constant term is written on the other side. The standard form is useful for graphing and finding the x- and y-intercepts of a line.

Why Convert to Slope-Intercept Form?

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept. This form is useful for finding the slope and y-intercept of a line, as well as for graphing the line.

The Step-by-Step Process of Converting to Slope-Intercept Form

To convert the equation 4x + 3y = 9 to slope-intercept form, we need to isolate y on one side of the equation. Here are the steps:

1. Subtract 4x from both sides of the equation: 4x + 3y = 9 3y = -4x + 9

2. Divide both sides of the equation by 3: y = (-4/3)x + 3

Understanding the Slope and Y-Intercept

Now that we have the equation in slope-intercept form, we can identify the slope and y-intercept.

• The slope (m) is -4/3, which means that for every 1-unit increase in x, the value of y decreases by 4/3 units.
• The y-intercept (b) is 3, which means that the line intersects the y-axis at the point (0, 3).

Graphing the Line

To graph the line, we can use the slope and y-intercept. We can start by plotting the y-intercept (0, 3), and then use the slope to find another point on the line.

For example, if we move 1 unit to the right (x = 1), the value of y will decrease by 4/3 units. Therefore, the new point will be (1, 3 - 4/3) = (1, 5/3).

Real-World Applications of Slope-Intercept Form

The slope-intercept form of a linear equation has many real-world applications, such as:

• Cost analysis: The slope of a line can represent the cost per unit of a product, while the y-intercept represents the fixed cost.
• Physics: The slope of a line can represent the velocity of an object, while the y-intercept represents the initial position.

Common Mistakes to Avoid

When converting an equation to slope-intercept form, there are several common mistakes to avoid:

• Forgetting to distribute the negative sign when subtracting a term from both sides of the equation.
• Forgetting to divide both sides of the equation by the coefficient of y.
• Not checking the units of the slope and y-intercept.

Conclusion

In conclusion, converting an equation from standard form to slope-intercept form can be made easy by following a step-by-step process. By understanding the slope and y-intercept, we can graph the line and apply it to real-world problems. Remember to avoid common mistakes and always check your units.

We hope this article has been helpful in explaining how to convert the equation 4x + 3y = 9 to slope-intercept form. If you have any questions or need further clarification, please leave a comment below.