All Things Linear

Function

Definition - relationship where each INDEPENDENT set is associated with exactly ONE value from the dependent (OUTPUT/range/Y-COORDINATE)

Attributes

• X-coordinates CANNOT repeat but the Y-coordinates CAN repeat
• must pass the VERTICAL line test
• examples include: patterns, tables, mappings, descriptions, equations, ordered pairs, & graphs
• can be LINEAR or non-LINEAR relationships

Linear

Definition - relationship between independent and DEPENDENT quantities that form a LINE when graphed on a coordinate plane

Attributes

• variables only have an exponent of 1
• no variables in the DENOMINATOR
• only need TWO points to find the EQUATION or graph
• can be continuous (CONNECTED) or DISCRETE (disconnected)
• has slope which can be positive, NEGATIVE, zero, or undefined

Slope

Definition - describes the DIRECTION and STEEPNESS of a line

Attributes

• the change in Y-coordinate compared to the change in X-coordinate
• EQUIVALENT for any 2 points
• SIMILAR triangles have equivalent RATIOS
• right triangles that share a HYPOTENUSE
• represented by the variable, m

Intercepts

Y-Intercept

• ordered pair where the line INTERSECTS the Y-axis
• represented by the variable, b
• X-coordinate is always zero (0,b)

X-Intercept

• ordered pair where the line intersects the X-axis
• NOT represented by a variable
• Y-coordinate is always zero (x-int,0)
• also called the ZERO

Equation Forms

y=mx+b

equation of a line using the SLOPE, m, and Y-INTERCEPT, b

Ax+By=C

equation of a line where A, B, and C are INTEGERS and A must be positive

Differences

Constant Rate of Change, a

Slope, m

Constant of Proportionality, k

CONSTANT OF PROPORTIONALITY, k
unit rate
scale factor
equivalent ratios