Question

Standard form to slope intercept form

Answer 1

To convert a linear equation from standard form to slope-intercept form, which is in the form
`\(y = mx + b\)`, where
`\(m\)` is the slope and
`\(b\)` is the y-intercept, follow below steps.

To convert a linear equation from standard form to slope-intercept form, which is in the form
`\(y = mx + b\)`, where
`\(m\)` is the slope and
`\(b\)` is the y-intercept, we can follow these steps:

1. Standard Form of a Linear Equation:

Standard form looks like this:
`\(Ax + By = C\)`, where
`\(A\), \(B\), and \(C\)`are constants, and
`\(A\)` is usually a positive integer.

2. Isolate
`\(y\)`:

Our goal is to get the equation in the form
`\(y = mx + b\)`, so isolate
`\(y\)` on one side of the equation. If the equation is in the standard form
`\(Ax + By = C\)`, subtract
`\(Ax\)` from both sides.

Example:
`\(2x - 3y = 7\)`

`\[ -3y = -2x + 7 \]`

3. Divide by the Coefficient of
`\(y\):`

Once
`\(y\)` is on one side, divide both sides by the coefficient of
`\(y\)` to make it 1.

Example:
`\[y = (2)/(3)x - (7)/(3)\]`

4. Adjust the Form:

If needed, rearrange the equation to make it look more like
`\(y = mx + b\).`

Example:
`\[y = (2)/(3)x - (7)/(3)\]`

Multiply through by 3 to clear the fraction:

`\[3y = 2x - 7\]`

The final slope-intercept form is
`\(y = (2)/(3)x - (7)/(3)\)`.

The probable question may be:

"How to convert standard form to slope intercept form?"