Strategy: Choosing a Method for Graphing Standard Form
Grade 8 math students learn a decision strategy for graphing linear equations in standard form Ax + By = C, choosing between using x and y intercepts (when A and B divide evenly into C) or converting to slope-intercept form (when intercepts are fractions). This strategic thinking saves time and improves accuracy. Covered in Big Ideas Math, Course 3, Chapter 4: Graphing and Writing Linear Equations.
Key Concepts
When graphing a linear equation in standard form, $Ax + By = C$, you can choose between two primary methods. Use this table as a guide:.
| Method | Best to Use When... | | : | : | | Using x and y intercepts | The coefficients $A$ and $B$ are factors of the constant $C$. This results in integer intercepts that are easy to plot. | | Converting to Slope Intercept Form | The intercepts are not integers (i.e., $A$ or $B$ are not factors of $C$), or when it is very easy to isolate $y$ (e.g., when $B=1$ or $B= 1$). |.
Common Questions
When should you use intercepts to graph standard form?
Use intercepts when the coefficients A and B are both factors of the constant C. This gives integer intercepts that are easy to plot accurately on the coordinate plane.
When should you convert standard form to slope-intercept form?
Convert to slope-intercept form when A or B do not divide evenly into C, producing fraction intercepts that are hard to graph. It is also better when B equals 1 or -1 making isolation of y easy.
What is the standard form of a linear equation?
Standard form is Ax + By = C. To graph it, you can find the x-intercept (set y=0, solve for x) and y-intercept (set x=0, solve for y), or convert to slope-intercept form y = mx + b.
Which textbook covers graphing strategies for standard form for Grade 8?
This topic is in Big Ideas Math, Course 3, Chapter 4: Graphing and Writing Linear Equations.
What grade level covers graphing linear equations in standard form?
Graphing strategies for standard form equations are typically covered in Grade 8 math.