Linear Equation Summary

Open Intercept Form of Linear Equation

• Discussed slope-intercept form: $y = mx + b$ (where $m$ is slope, and $b$ is y-intercept).
• Emphasized the importance of writing equations in this form.

Slope and Y-Intercept

• Slope ($m$) shows the steepness; can be determined as the coefficient of $x$.
• Y-intercept ($b$) is the point where the line crosses the y-axis.

Steps for Graphing Lines

1. Write the equation in slope-intercept form ($y = mx + b$).
2. Identify the y-intercept (point $(0, b)$).
3. Determine the slope $m$ (rise/run) to find another point.
4. Draw the line through the points.

Horizontal and Vertical Lines

• Horizontal Line: has a slope of 0; equation format: $y = b$.
• Vertical Line: has an undefined slope; equation format: $x = a$.

Example Calculations

• Slope for line $y = 2x + 3$ is 2, and y-intercept is 3.
• Concrete example: For $3x - 4y = 0$, rearranged to slope-intercept gives slope = 3/4.
• Additional graphical exercises involve finding points using given slopes and intercepts.