To find the slope and the y-intercept of a line given in the standard form, you can follow the steps below. The standard form of a line is usually written as:
Ax + By = C
Where A, B, and C are constants.
Step 1: Rewrite in Slope-Intercept Form
The slope-intercept form of a line is:
y = mx + b
Where:
- m: the slope of the line
- b: the y-intercept of the line
To convert the standard form into the slope-intercept form, isolate y. For example:
Given the equation:
3x + 2y = 12
Subtract 3x from both sides:
2y = -3x + 12
Now, divide everything by 2:
y = -3/2x + 6
Step 2: Identify the Slope and Y-Intercept
From the equation y = -3/2x + 6, we can identify:
- The slope (m) is -3/2
- The y-intercept (b) is 6
Conclusion: In this example, the slope of the line is -3/2, and the y-intercept is 6. You can apply the same method to any linear equation in standard form to find its slope and y-intercept.