Converting Linear Equations: Standard Form to Slope-Intercept Form and Vice Versa

standard and slope intercept

The standard form of a linear equation is written as Ax + By = C, where A, B, and C are constants

The standard form of a linear equation is written as Ax + By = C, where A, B, and C are constants.

The slope-intercept form of a linear equation is written as y = mx + b, where m represents the slope and b represents the y-intercept.

To convert from standard form to slope-intercept form, you can follow these steps:

1. Start with the standard form equation: Ax + By = C.

2. Solve the equation for y by subtracting Ax from both sides: By = -Ax + C.

3. Divide both sides by B to isolate y: y = (-A/B)x + (C/B).

Now, you can see that the equation is in slope-intercept form, where the slope is -A/B and the y-intercept is C/B.

To convert from slope-intercept form to standard form, you can follow these steps:

1. Start with the slope-intercept form equation: y = mx + b.

2. Multiply both sides of the equation by the denominator of the slope (m) to eliminate any fractions: my = mx + mb.

3. Rearrange the terms to have all variables on one side and constants on the other side: mx – my = -mb.

Now, you have the equation in standard form, where A = m, B = -m, and C = -mb.

In summary, the standard form of a linear equation is Ax + By = C, and the slope-intercept form is y = mx + b. Converting between these two forms involves manipulating the equations to isolate y or rearrange the terms into the proper form.

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