How to find slope intercept form

Imagine you’re sitting in a high school algebra class, trying to grasp the concepts of linear equations. Your teacher just introduced the idea of slope-intercept form, but all the terminology feels overwhelming. You’ve got a sheet full of linear equations, and you’re determined to figure out how to convert them into the slope-intercept form \(y = mx + b\) where \(m\) is the slope and \(b\) is the y-intercept. As you look around, you’re not alone; many of your classmates share the same confusion. You can’t help but wonder, how exactly do you find the slope-intercept form?

To find the slope-intercept form of a linear equation, you need to rearrange the equation into the format \(y = mx + b\), where \(m\) represents the slope and \(b\) is the y-intercept.

To convert an equation into slope-intercept form, start with the standard form of the equation, usually written as \(Ax + By = C\). The goal is to isolate \(y\) on one side of the equation. Here are the steps you can follow:

1. Start with the original equation: Identify the equation that you need to convert. For example, suppose you have \(2x + 3y = 6\).

2. Isolate the \(y\)-term: Subtract the \(x\)-term from both sides. Using the example, you would rearrange the equation to:

\[

3y = -2x + 6

\]

3. Solve for \(y\): Divide each term by the coefficient of \(y\). In our example, we divide by 3:

\[

y = -\frac{2}{3}x + 2

\]

4. Identify the slope and y-intercept: Now, the equation is in slope-intercept form \(y = mx + b\), where \(m = -\frac{2}{3}\) (the slope) and \(b = 2\) (the y-intercept).

By following these steps, you can convert any linear equation into slope-intercept form, making it easier to graph or analyze its characteristics!