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