Slope Intercept and Graphing

slope

"Rise over run"

linear function

A function whose graph is a line and for every x-value there is only one y-value

ordered pair

A pair of numbers that give the location of a point on a x and y grid. for example graph (3, 2)

coordinate plane

A plane that is divided into four regions by a horizontal line called the x-axis and a vertical line called the y-axis.

scale (on a graph)

A series of numbers at equal distances along an axis on a graph.

Line

A set of points that extends without end in two opposite directions

solution of an equation

A value that makes an equation true. 6 is the solution of the equation x - 4 = 2

Cartesian Plane

Another name for COORDINATE PLANE

linear equation

an equation whose graph is a straight line

origin

is represented by the ordered pair (0, 0), and it has both x- and y-coordinates of 0.

quadrant

one of four sections into which the coordinate plane is divided

Slope Formula, given 2 points

rise/run or change in y over change in x; Given two points (x1, y1) and (x2, y2), slope is found using the formula m = (y2 - y1)/(x2 - x1)

plotting points

the act of drawing points on a graph, using the ordered pair to locate the points

x-coordinate

the first number in an ordered pair

x-axis

the horizontal axis on a coordinate plane

y-coordinate

the second number in an ordered pair

slope

the steepness of a line on a graph, equal to its vertical change divided by its horizontal change

y-axis

the vertical axis on a coordinate plane

y-intercept

the y-coordinate of a point where a graph crosses the y-axis

slope-intercept form

y=mx+b, where m is the slope and b is the y-intercept of the line.

b

The variable that represents the y-intercept of a line, in a linear equation

f(x) notation

Function notation where f is the name of the function and x is the input; for example if f(x) = x + 2, then f(3) = 3 + 2 = 5.

Graphing by intercepts

One way to graph a function; find the x-intercept (set y = 0 and solve) and the y-intercept (set x = 0 and solve); plot the intercepts and connect.

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.

Slope-Intercept Graphing Method

Put a linear equation in slope-intercept form (y = mx + b); plot the y-intercept; use the slope ratio to find other points relative to the y-intercept (make slope a fraction - numerator is change in y (up or down), denominator is change in x (left or right)).

Ax + By = C

Standard form of a linear equation, where A, B, and C represent constant numbers and x and y represent variables.

x-intercept

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

domain of a function

The set of all possible input values (x-values) for the function

Range of a function

The set of all possible output values (y-values)of a function

0 slope

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

negative slope

The slope of a line that decreases as x-values increase (points go down left to right).

positive slope

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

undefined slope

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

m

The variable in slope-intercept form that represents the slope of the linear equation