The slope-intercept form of a linear equation is one of the most common and useful forms in mathematics and science. It's represented as y = mx + b, where m is the slope of the line and b is the y-intercept. Converting an equation to slope-intercept form can make it easier to understand and work with. In this article, we'll explore how to convert the equation 2x + 3y = 9 to slope-intercept form.
Why Convert to Slope-Intercept Form?
Converting an equation to slope-intercept form has several advantages. It allows us to:
- Easily identify the slope and y-intercept of the line
- Determine the direction and steepness of the line
- Find the equation of a line given the slope and a point on the line
- Graph the line using the slope and y-intercept
How to Convert 2x + 3y = 9 to Slope-Intercept Form
To convert the equation 2x + 3y = 9 to slope-intercept form, we need to isolate y on one side of the equation.
Step 1: Rearrange the Equation
Start by rearranging the equation to have all the terms with y on one side:
2x + 3y = 9
Subtract 2x from both sides:
3y = -2x + 9
Step 2: Divide Both Sides by 3
Next, divide both sides of the equation by 3 to isolate y:
y = (-2x + 9) / 3
y = -2/3x + 3
Slope-Intercept Form
The equation is now in slope-intercept form: y = mx + b, where m = -2/3 and b = 3.
In this form, we can see that the slope of the line is -2/3, which means that for every 3 units we move to the right, the line goes down by 2 units. The y-intercept is 3, which means that the line crosses the y-axis at the point (0, 3).
Key Takeaways
- The slope-intercept form of a linear equation is y = mx + b.
- To convert an equation to slope-intercept form, isolate y on one side of the equation.
- The slope (m) and y-intercept (b) can be easily identified in slope-intercept form.
Practical Applications
Converting equations to slope-intercept form has numerous practical applications in science, engineering, and mathematics. For example:
- In physics, slope-intercept form can be used to model the motion of objects, where the slope represents the velocity and the y-intercept represents the initial position.
- In economics, slope-intercept form can be used to model supply and demand curves, where the slope represents the elasticity of demand and the y-intercept represents the equilibrium price.
Conclusion
Converting the equation 2x + 3y = 9 to slope-intercept form is a straightforward process that involves isolating y on one side of the equation. By rearranging the equation and dividing both sides by 3, we can easily identify the slope and y-intercept of the line. This form is useful for understanding the direction and steepness of the line, as well as for graphing the line and finding the equation of a line given the slope and a point on the line.
We hope this article has helped you understand how to convert an equation to slope-intercept form. If you have any questions or need further clarification, please don't hesitate to ask.
What is slope-intercept form?
+Slope-intercept form is a way of writing a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept.
Why is slope-intercept form useful?
+Slope-intercept form is useful because it allows us to easily identify the slope and y-intercept of a line, which can be used to understand the direction and steepness of the line.
How do I convert an equation to slope-intercept form?
+To convert an equation to slope-intercept form, isolate y on one side of the equation by rearranging the terms and dividing both sides by the coefficient of y.