Transforming standard form equations into slope-intercept form is an important skill in Grade 10 Algebra I.

The slope-intercept form looks like this: $y = mx + b$ In this formula, $m$ is the slope of the line, and $b$ is where the line crosses the y-axis.

If you want to change an equation from standard form, which looks like this: $Ax + By = C$ into slope-intercept form, it’s a helpful step for graphing and understanding linear equations.

Steps to Change Standard Form to Slope-Intercept Form

1. Start with the Standard Form Equation: Let’s use an example: $2x + 3y = 6$

2. Isolate the $y$ Variable: To convert this equation, you need to solve for $y$. Start by getting the $2x$ term by itself on the other side: $3y = -2x + 6$

3. Divide by the Coefficient of $y$: Next, divide every part by 3 (the number in front of $y$): $y = -\frac{2}{3}x + 2$

   Now, we have the equation in slope-intercept form. Here, the slope $m$ is $-\frac{2}{3}$, and the y-intercept $b$ is 2.

Example Walkthrough

Let’s try another example to make sure we understand. Consider this equation: $4x - 2y = 8$

1. Rearrange the Equation: Move the $4x$ to the other side: $-2y = -4x + 8$

2. Divide by -2: Isolate $y$ by dividing by -2: $y = 2x - 4$

Now the slope $m$ is 2, and the y-intercept $b$ is -4.

Key Points to Remember

• Conversion: Changing from standard to slope-intercept form means isolating $y$.
• Recognizing Forms: Slope-intercept form shows the slope and the y-intercept clearly, which makes graphing easier.
• Practice: The more you work on these conversions, the better you will understand them.

Changing standard form equations to slope-intercept form can help you understand how lines work. It also sets up a good foundation for studying more about linear equations and how they apply in real life. Happy graphing!