# Linear Equations & Graphs

## 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.

# Features of Linear Graphs:

- 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.

# Techniques for Sketching Linear 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 Linear Equations:

**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.

# Applications of Linear Equations:

- 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.