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Linear Equations and Functions
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Gravity
Linear Functions and Graphing. Vocabulary.
Terms in this set (40)
relation
A set of ordered pairs. Two quantities that are being compared.
domain
D: - The Domain, All Input values, the Independent variable.
range
R: - The Range, All Output values, the Dependent variable.
function
A special relation, where each input or X-value, has a unique corresponding output, or y-value.
equation in two variables
An equation that represents two quantities that change in relationship to one another
vertical-line test
The test that visually determines whether or not a relation is a function or not.
linear function
is a function whose graph is a non-vertical line or part of a non-vertical line.
independent variable
The variable that is systematically manipulated by the researcher in an experiment. Typically graphed on the horizontal axis.
dependent variable
The experimental factor that is being measured; the variable that may change in response to manipulations of the independent variable. Typically graphed on the vertical axis.
linear equation
Any equation whose graph is a line.
function notation
When you use this, you use f(x) instead of y.
slope
The vertical change over the horizontal change
= rise/run
A ratio, rate, or relation that describes the tilt of a line.
solution
An ordered pair that makes an equation a true statement.
perpendicular lines
Lines whose slopes are opposites and reciprocals.
parallel lines
Two lines in the same plane that never intersect. Parallel lines have the same slope.
rate of change
the relationship between two quantities that are changing. The rate of change is also called slope. rate of change=change in the dependent variable/change in the independent variable.
parent function
The simplest, most general function in a family of functions.
y-intercept
The point where the line crosses the y-axis. Also, the constant in an equation that is in slope-intercept form (y = mx + b). Where x = 0.
x-intercept
x coordinate of a point where a graph crosses the x axis/ y coordinate of this point is zero
slope-intercept form
y = mx + b.
standard form of a linear equation
Ax + By= C
point-slope form
y-y1 = m(x-x1)
direct variation
A linear function defined by an equation of the form y = kx, where k does not equal 0.
constant of variation
The constant used with direct variation.
scatter plot
A graph that shows the relationship between two sets of data.
positive correlation
As one set of values increases, the other set tends to increase.
negative correlation
As one set of values increases, the other set tends to decrease
no correlation
The values show no relationship.
correlation coefficient
a number that expresses the degree and direction of the relationship between 2 variables, ranging from -1 to +1
best-fitting line
A line that closely fits the data points in the scatter plot.
absolute value function
A function with a V-shaped graph that opens up or down. The parent function for the family of absolute value functions is y = | x |.
vertex of an absolute value graph
the highest or lowest point on the graph of an absolute value function, (h,k).
translation
A shift of a graph horizontally, vertically, or both, which results in a graph of the same shape and size, but in a different position.
transformation
An operation that changes a graph's size, shape, or orientation.
reflection
A transformation that "flips" a figure over a mirror or reflection line.
linear inequality
When you replace the equal sign in a linear equation with >, <, ≥, or ≤, the result is this.
solution of a linear inequality
Any point, (x,y), that makes a linear inequality true
system of linear inequalities
Two ore more linear inequalities together.
solution of a system of linear inequalities
Any ordered pair that makes each inequality in the system true is a _.
half-plane
A half-plane is the graph of a linear inequality. If it is a strict inequality, ("less than" or "greater than", then the line is dashed to indicate that it is not included in the graph of the inequality. If it is not a strict inequality, ("less than or equal to" or "greater than or equal to"), then the line is solid.
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