Linear Functions - Morris

y-intercept

"b" in y = mx + b The place on the y-axis where the line touches or crosses (the x-value is always 0.) Example: (0,3)

System of Linear Equations

2 or more equations graphed or in a group

Average Rate of Change (Slope formula) in Function Notation

Change in "y"/Change in "x"

Ax + By = C Standard Form

Form of a linear equation, where A and B are coefficients of the variables x and y. C is a constant number.

slope formula

Name of the formula shown. You must use two solutions or ordered pairs to determine the value.

Function Notation

Notation where f(x) is the output of the function and x is the input; for example if f(x) = x + 2, then f(3) = 3 + 2 = 5.: f(3) = 5: or Point Form: (5,f(3)) When "x" is 3, f(x) is 5

Intercepts Graphing Method

One way to graph a function; find the "x" and "y" intercepts, graph, draw a line through them.

Table of Values Graphing Method

One way to graph a function; first find some x-values in the domain, and then calculate the y-values using the function rule; points can then be plotted and connected.

Parallel Lines

Same slope, different y-intercepts Example: y = 1/3x -4 y = 1/3x +5

"m" in the y=mx+b

Slope

y = mx + b

Slope-Intercept form of a linear equation, where "m" represents slope and "b" represents y-intercept.

Perpendicular Lines

Slopes are opposite reciprocal (a/b ---- > -b/a) Example: y = 2/3x -4 y = 3/2x +5

x-intercept

The place on the x-axis where the line touches or crosses (the y-value is always 0) Example: (4,0)

slope

The ratio of change between two points on a line. Rise/Run or change in y over change in x.

zero slope

The slope of a horizontal line (the change in y-values is 0).Example: 0/12

negative slope

The slope of a line that decreases as x-values increase (points go down left to right). Example: m = -1/2

positive slope

The slope of a line that increases as x-values increase (points go up left to right). Example: m = 5

undefined slope

The slope of a vertical line (cannot be found because it would force a division by 0, undefined in mathematics)-Example: 12/0

Slope-Intercept Graphing Method

Use the form y=mx+b, first graph the y-intercept, then use the slope to find another point, draw a line through the two points.

Point-Slope form of the linear Equation Version 1

Used to find the linear equation when given a point and a slope.

"b" in the y=mx+b

Y-intercept

Solution of a system of equations

point of intersection on the graph

What is the value of x on the y-axis?

x = 0

What is the value of "y" on the x-axis?

y = 0

Point-Slope form of a linear equation Version 2 Helps to understand Function Transformations

y = m(x - h) + k m = slope (h,k) is any point on the line

Slope-Intercept Form of a linear equation

y = mx + b