Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. When graphed, it forms a straight line.

Slope-Intercept Form

The standard form of a linear equation is $Ax + By = C$ . However, the Slope-Intercept Form is often more useful for graphing:

$y = mx + b$

Where:

$m$ is the slope (gradient) of the line, calculated as $\frac{\text{rise}}{\text{run}}$ .
$b$ is the y-intercept (where the line crosses the y-axis).

Interactive Visualizer

Experiment with the slope ( $m$ ) and y-intercept ( $b$ ) to see how they affect the line graph. Notice how a positive slope goes "uphill" and a negative slope goes "downhill".

Solving Linear Equations

To solve for a variable, isolate it on one side of the equation using inverse operations. Remember: whatever you do to one side, you must do to the other.

Solving Inequalities

Solving linear inequalities (like $3x < 9$ ) follows the same rules as equations, with one crucial exception:

If you multiply or divide both sides by a negative number, you must flip the inequality sign.

Example: $-2x > 6 \implies x < -3$ .

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