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

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Converting a linear equation from standard form to slope-intercept form is a fundamental concept in algebra. The slope-intercept form, y = mx + b, is a valuable representation of a linear equation because it reveals the slope (m) and the y-intercept (b) of the line, providing insights into its behavior and appearance on the graph.

Let's take the given linear equation 2x + 4y = 5 and convert it into slope-intercept form in three straightforward steps.

Step 1: Isolate the Term with y on One Side

To begin converting the equation 2x + 4y = 5 into slope-intercept form, we first need to isolate the term involving y on one side of the equation. We can do this by subtracting 2x from both sides of the equation. This step keeps the equation balanced while moving the x term to the other side.

2x + 4y = 5  
Subtract 2x from both sides:  
4y = -2x + 5

Step 2: Solve for y

Now that we have isolated the term with y on one side, we can solve for y. This involves dividing both sides of the equation by the coefficient of y, which in this case is 4. Dividing by 4 will leave y alone on the left side of the equation.

4y = -2x + 5  
Divide both sides by 4:  
y = (-2/4)x + 5/4  
Simplify the fractions:  
y = -1/2x + 5/4

Step 3: Write in Slope-Intercept Form

After solving for y, we now have the equation in slope-intercept form, which is y = mx + b. Here, m is the slope of the line (-1/2 in our case), and b is the y-intercept (5/4). The equation y = -1/2x + 5/4 is in the desired slope-intercept form.

Benefits of Slope-Intercept Form

Converting linear equations to slope-intercept form offers several benefits:

• Easier Graphing: Knowing the slope (m) and y-intercept (b) makes graphing the line straightforward. You can start at the y-intercept and use the slope to find other points.
• Slope Analysis: The slope provides insights into the line's behavior, including whether it's increasing or decreasing, and how steep it is.
• Equation Comparison: Slope-intercept form makes it easy to compare different linear equations based on their slopes and y-intercepts.

Conclusion

Converting a linear equation from standard form to slope-intercept form is a practical skill that enhances understanding and analysis of linear relationships. By following these steps, you can easily convert equations and gain valuable insights into their graphical and analytical properties.

Invite readers to practice converting linear equations to slope-intercept form using the steps outlined in this article. Share your experiences or ask questions about the process in the comments below!