To change linear function equations between standard form and slope-intercept form, it's important to know what each form means first.
Standard Form: This form looks like ( Ax + By = C ). Here, ( A ), ( B ), and ( C ) are whole numbers (integers), and ( A ) should be a positive number.
Slope-Intercept Form: This form is written as ( y = mx + b ). In this case, ( m ) represents the slope, and ( b ) is where the line crosses the y-axis (the y-intercept).
How to Change Standard Form to Slope-Intercept Form: Let’s take the standard form equation: [ 2x + 3y = 6. ] To change this to slope-intercept form, we need to solve for ( y ):
First, subtract ( 2x ) from both sides: [ 3y = -2x + 6. ]
Next, divide every term by ( 3 ): [ y = -\frac{2}{3}x + 2. ] In this example, the slope (( m )) is (-\frac{2}{3}) and the y-intercept (( b )) is (2).
How to Change Slope-Intercept Form to Standard Form: Now, let’s try it the other way. Starting from the slope-intercept form: [ y = \frac{1}{2}x - 4, ] we can eliminate the fraction by multiplying everything by ( 2 ): [ 2y = x - 8. ] Now, let’s rearrange it: [ -x + 2y = -8, ] or if we multiply by (-1): [ x - 2y = 8. ]
Now you know how to easily switch between these two forms!
To change linear function equations between standard form and slope-intercept form, it's important to know what each form means first.
Standard Form: This form looks like ( Ax + By = C ). Here, ( A ), ( B ), and ( C ) are whole numbers (integers), and ( A ) should be a positive number.
Slope-Intercept Form: This form is written as ( y = mx + b ). In this case, ( m ) represents the slope, and ( b ) is where the line crosses the y-axis (the y-intercept).
How to Change Standard Form to Slope-Intercept Form: Let’s take the standard form equation: [ 2x + 3y = 6. ] To change this to slope-intercept form, we need to solve for ( y ):
First, subtract ( 2x ) from both sides: [ 3y = -2x + 6. ]
Next, divide every term by ( 3 ): [ y = -\frac{2}{3}x + 2. ] In this example, the slope (( m )) is (-\frac{2}{3}) and the y-intercept (( b )) is (2).
How to Change Slope-Intercept Form to Standard Form: Now, let’s try it the other way. Starting from the slope-intercept form: [ y = \frac{1}{2}x - 4, ] we can eliminate the fraction by multiplying everything by ( 2 ): [ 2y = x - 8. ] Now, let’s rearrange it: [ -x + 2y = -8, ] or if we multiply by (-1): [ x - 2y = 8. ]
Now you know how to easily switch between these two forms!