Linear Equation
This Grade 6 algebra skill from Yoshiwara Elementary Algebra introduces the definition and standard form of a linear equation. Students learn that a linear equation is an algebraic equation of degree 1 whose graph is always a straight line, typically written in forms such as y = mx + b or ax + by = c.
Key Concepts
Property An equation of the form $y = ax + b$, where $a$ and $b$ are constants, is called a linear equation because its graph is a straight line. We can graph a linear equation by evaluating the expression $ax + b$ at several values of $x$ and then plotting the resulting points.
Examples A sapling is 5 inches tall and grows 2 inches each week. The height $H$ after $w$ weeks is given by the equation $H = 5 + 2w$. After 3 weeks, the height is $H = 5 + 2(3) = 11$ inches.
You are 200 miles from home and driving away at 60 miles per hour. Your distance $D$ from home after $h$ hours is $D = 200 + 60h$. After 2 hours, the distance is $D = 200 + 60(2) = 320$ miles.
Common Questions
What is a linear equation?
A linear equation is an equation where the highest power of the variable is 1. Its graph is always a straight line, and common forms include y = mx + b and ax + by = c.
What makes an equation linear?
An equation is linear if no variable is raised to a power other than 1, and no variables are multiplied together. For example, 2x + 3 = 7 is linear, but x^2 = 4 is not.
What are the common forms of a linear equation?
The slope-intercept form is y = mx + b. The standard form is ax + by = c. Both represent straight lines.
How many solutions does a linear equation in two variables have?
A linear equation in two variables has infinitely many solutions—every point on its graph is a solution.
Where is the linear equation definition taught?
Linear equations are introduced in the Yoshiwara Elementary Algebra textbook for Grade 6.