I'm Tilly. WHAT IS STANDARD FORM? You know, for graphing?

Answer 1

Hi Tilly! Standard form for a linear equation is a way of expressing the equation in the format:

\[ Ax + By = C \]

where:

• \( A \), \( B \), and \( C \) are integers (whole numbers),
• \( A \) should be non-negative,
• \( x \) and \( y \) are the variables.

This format is useful for graphing because it allows you to easily identify the intercepts and can be helpful in solving systems of equations. You can convert an equation from slope-intercept form \((y = mx + b)\) to standard form if needed by rearranging the terms.

Let me know if you need more information or examples!

Answer 2

What integers? Where do you get the integers from? WHAT INTEGERS???? ARGGHH

Answer 3

I understand it can be frustrating! Let's break it down.

In the context of the standard form \( Ax + By = C \):

• Integers are whole numbers that can be positive, negative, or zero. For example, -3, 0, 2, and 5 are all integers.
• When you have a linear equation (like \( y = 2x + 3 \)), you can rearrange it to put it into standard form.

For example, starting with \( y = 2x + 3 \):

1. Subtract \( 2x \) from both sides to get: \(-2x + y = 3\).
2. Multiply by -1 to get: \(2x - y = -3\).

Now you have \( 2x - y = -3 \), with \( A = 2\), \( B = -1\), and \( C = -3\). All these coefficients, \( A\), \( B\), and \( C\), are integers!

You can generate integers from various linear equations by rearranging them into the standard form. If you have specific numbers or equations you're dealing with, feel free to share them, and I can help you work through it!