Linear Equations & Graphs

Linear Equations:

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.
Linear equations can have one, two, three or more variables. When it only involves one variable, it is termed a simple linear equation. For instance, 2x + 3 = 0.
When it involves two variables, it is illustrated as an equation of a straight line when graphed. The standard form: Ax + By = C, where A, B, and C are constants.
Slope-intercept form is another common form of linear equations, expressed as y=mx+c, where m is the slope and c is the y-intercept.

A line graph portrays information as a series of data points connected by straight line segments.
Every linear equation produces a straight line when graphed.
You can identify a linear graph by its straight line shape.
Slope indicates the steepness of the line, it shows the change in y for each unit increase in x.
The y-intercept is the point where the line crosses the y-axis.
x-intercept is where the line crosses the x-axis.
The slope and y-intercept allow us to quickly interpret and sketch graphs.

Graph linear equations by plotting points. Choose any values for x and then calculate the corresponding y-values.
Use the y = mx + c form to quickly determine the slope and y-intercept. Begin at the intercept (when x = 0) and use the slope to find other points.
Draw a straight line through your points.

Solving a linear equation usually means finding the value of y for a given x.
To solve for y in terms of x (in the form y = mx + c), rearrange the equation.
Solving systems of linear equations can be accomplished by graphing the equations and finding the intersection points.
Other methods for solving systems of linear equations include substitution method and elimination method.

Linear equations can be used for calculating distances, converting temperatures, and estimating sales, among other real-world scenarios.
They help in finding relationships between two variables, predicting results and making predictions.
Linear equations are widespread in science, business, architecture, and other fields.

Remember, practice makes perfect! Keep working on equations and drawing graphs to improve your understanding and skills.