Convert 3x 2y 4 To Slope Intercept Form In 5 Steps

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Converting a linear equation from standard form to slope-intercept form can be a straightforward process. Let's dive into the steps to convert the given equation, 3x 2y 4, to slope-intercept form.

The Importance of Slope-Intercept Form

Before we begin, let's quickly discuss why slope-intercept form is so useful. The slope-intercept form of a linear equation, y = mx + b, provides a clear understanding of the line's slope (m) and y-intercept (b). This form makes it easy to identify the line's steepness and the point at which it crosses the y-axis.

Step 1: Rewrite the Equation

First, let's rewrite the given equation, 3x 2y 4, in a more familiar form. To do this, we'll rearrange the terms to have all the variables on one side and the constants on the other.

This gives us: 2y = 3x + 4

Step 2: Isolate the y-Variable

Next, we'll isolate the y-variable by dividing both sides of the equation by 2.

This gives us: y = (3/2)x + 2

Step 3: Identify the Slope and y-Intercept

Now that we've isolated y, we can identify the slope (m) and y-intercept (b) of the line. In this case, the slope is 3/2, and the y-intercept is 2.

Step 4: Write the Equation in Slope-Intercept Form

The equation is now in slope-intercept form: y = (3/2)x + 2. This form makes it easy to understand the line's slope and y-intercept.

Step 5: Verify the Result

Finally, let's verify our result by checking that the equation is indeed in slope-intercept form. We can do this by plugging in a value for x and solving for y.

For example, if we plug in x = 2, we get: y = (3/2)(2) + 2 = 5

Example Use Cases

Now that we've converted the equation to slope-intercept form, let's consider some example use cases.

• Finding the equation of a line given its slope and y-intercept
• Graphing a line using its slope and y-intercept
• Solving systems of linear equations using substitution or elimination

Common Challenges

When converting equations to slope-intercept form, some common challenges include:

• Forgetting to isolate the y-variable
• Incorrectly identifying the slope and y-intercept
• Not verifying the result

Practical Applications

Converting equations to slope-intercept form has many practical applications, including:

• Physics: modeling the motion of objects using linear equations
• Engineering: designing systems using linear equations
• Economics: modeling economic systems using linear equations

Key Takeaways

To convert an equation to slope-intercept form, follow these steps:

1. Rewrite the equation to have all variables on one side and constants on the other.
2. Isolate the y-variable by dividing both sides by the coefficient of y.
3. Identify the slope and y-intercept.
4. Write the equation in slope-intercept form.
5. Verify the result.

By following these steps, you'll be able to convert equations to slope-intercept form with ease.

Conclusion

Converting equations to slope-intercept form is a valuable skill that can help you better understand and work with linear equations. By following the steps outlined in this article, you'll be able to convert equations with confidence. Remember to practice, practice, practice to become proficient in converting equations to slope-intercept form.