Converting the equation 3x 2y = 12 to slope-intercept form can be achieved through a series of steps. Slope-intercept form, which is expressed as y = mx + b, is a convenient way to represent linear equations. Here's how to do it in 5 steps:
Step 1: Understanding the Given Equation
The given equation is 3x - 2y = 12. The goal is to convert this equation into slope-intercept form, which will help us easily identify the slope (m) and the y-intercept (b) of the line.
Step 2: Isolate the Variable y
To convert the given equation to slope-intercept form, we need to isolate the variable y. This involves moving all terms involving y to one side of the equation and everything else to the other side.
Starting with the given equation: 3x - 2y = 12
Subtract 3x from both sides: -2y = -3x + 12
Step 2.1: Dividing Both Sides by -2
To solve for y, we need to get y by itself. Divide both sides of the equation by -2:
y = (-3x + 12) / -2
y = (3x - 12) / 2
Step 3: Simplifying the Equation
The equation y = (3x - 12) / 2 can be simplified further:
y = (3/2)x - 6
This equation is now in slope-intercept form.
Step 4: Identifying the Slope and Y-Intercept
In slope-intercept form, the equation y = mx + b allows us to easily identify the slope (m) and the y-intercept (b).
Comparing the equation y = (3/2)x - 6 to y = mx + b:
- The slope (m) is 3/2.
- The y-intercept (b) is -6.
Step 5: Verifying the Solution
To verify the solution, we can plug the slope-intercept form equation back into the original equation to ensure it's true:
3x - 2y = 12
Substitute y = (3/2)x - 6 into the equation:
3x - 2((3/2)x - 6) = 12
Expanding and simplifying:
3x - 3x + 12 = 12
This simplifies to:
12 = 12
Which is true.
Conclusion
The equation 3x - 2y = 12 has been successfully converted to slope-intercept form: y = (3/2)x - 6. The slope of the line is 3/2, and the y-intercept is -6. By following these steps, you can convert any linear equation in standard form to slope-intercept form.
What is slope-intercept form?
+Slope-intercept form is a way of expressing linear equations in the format y = mx + b, where m is the slope and b is the y-intercept.
How do I identify the slope and y-intercept in slope-intercept form?
+In slope-intercept form, the slope (m) is the coefficient of x, and the y-intercept (b) is the constant term.
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 graph the line and solve problems.