Algebra 1 Unit 4: Graphing Flashcards

Graph Concepts

• A graph represents a set of solutions (x, y) that satisfy an equation.
• Linear equations produce straight lines with constant slopes, while non-linear equations yield curves with varying slopes.

Key Definitions

• Table of Values: A collection of ordered pairs representing solutions to an equation.
• Slope-Intercept Form: The equation of a line is written as ( y = mx + b ) where:
  • ( m ) is the slope,
  • ( b ) is the y-intercept.

Intercepts

• Y-Intercept: Occurs when ( x = 0 ); represented as the point (0, b).
• X-Intercept: Found by setting ( y = 0 ) in the equation.

Graphing Techniques

• To graph a linear equation, determine the position (any point on the line) and direction (slope).
• Steps for graphing using slope-intercept form:
  • Ensure equation is in slope-intercept form.
  • Plot the y-intercept on the coordinate plane.
  • Use the slope to find additional points:
    • Slope in fraction form indicates movement (up/down for the numerator, right/left for the denominator).

Lines and Slopes

• Points are collinear if they lie on the same line with identical slopes.
• The slope formula: For points (x1, y1) & (x2, y2), slope ( m = \frac{y2 - y1}{x2 - x1} ).
• Classifications of lines by slope:
  • Positive slope: Rises from left to right.
  • Negative slope: Falls from left to right.
  • Zero slope: Horizontal line.
  • Undefined slope: Vertical line.

Line Equations

• Vertical Line: Written as ( x = a ) where all coordinates have the same value.
• Horizontal Line: Written as ( y = b ) where all y-values are constant.

Using Intercepts for Graphing

• Find the x-intercept by setting ( y = 0 ) and solve for ( x ).
• Find the y-intercept by setting ( x = 0 ) and solve for ( y ).
• Plot both intercepts and connect them with a line, adding arrowheads for direction.

Slope-Intercept Utility

• The slope-intercept equation ( y = mx + b ) is vital for:
  • Sketching graphs,
  • Determining the slope,
  • Identifying the y-intercept of a line.