Converting a linear equation from standard form to slope-intercept form is a crucial skill in algebra. The equation 2x - 3y = 9 can be converted to slope-intercept form using various methods. In this article, we will explore three ways to convert 2x - 3y = 9 to slope-intercept form.
Method 1: Solving for y
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. To convert 2x - 3y = 9 to slope-intercept form using this method, we need to isolate y on one side of the equation.
2x - 3y = 9
Subtract 2x from both sides:
-3y = -2x + 9
Divide both sides by -3:
y = (2/3)x - 3
Understanding the Slope and y-Intercept
In the slope-intercept form, the coefficient of x is the slope (m). In this case, the slope is 2/3. The constant term is the y-intercept (b), which is -3.
Method 2: Using the Slope Formula
Another way to convert 2x - 3y = 9 to slope-intercept form is by using the slope formula. The slope formula is m = (y2 - y1) / (x2 - x1), but since we don't have two points, we can use the coefficient of x and the constant term to find the slope.
2x - 3y = 9
Rearrange the equation to make y the subject:
-3y = -2x + 9
Divide both sides by -3:
y = (2/3)x - 3
The slope is 2/3, which is the coefficient of x.
Method 3: Graphical Method
The third method to convert 2x - 3y = 9 to slope-intercept form is by using the graphical method. This method involves graphing the equation on a coordinate plane and finding the slope and y-intercept.
2x - 3y = 9
Graph the equation:
From the graph, we can see that the y-intercept is -3 and the slope is 2/3. Using this information, we can write the equation in slope-intercept form:
y = (2/3)x - 3
Comparison of Methods
All three methods can be used to convert 2x - 3y = 9 to slope-intercept form. However, the first method (solving for y) is the most straightforward and widely used. The second method (using the slope formula) is useful when you don't have two points. The third method (graphical method) is helpful when you need to visualize the equation.
In conclusion, converting 2x - 3y = 9 to slope-intercept form is a simple process that can be done using various methods. Understanding the different methods can help you become more proficient in algebra and problem-solving.
We hope this article has helped you understand how to convert 2x - 3y = 9 to slope-intercept form. If you have any questions or need further clarification, please leave a comment below. Share this article with your friends and classmates who may benefit from it.
What is the slope-intercept form of a linear equation?
+The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
How do you convert a linear equation from standard form to slope-intercept form?
+To convert a linear equation from standard form to slope-intercept form, you need to isolate y on one side of the equation. This can be done by adding or subtracting the same value to both sides of the equation, and then dividing both sides by the coefficient of y.
What is the slope formula?
+The slope formula is m = (y2 - y1) / (x2 - x1), but since we don't have two points, we can use the coefficient of x and the constant term to find the slope.