Unit 2, lesson 1-6 : Linear Equations and Functions
ordered pair
A pair of numbers that can be used to locate a point on a coordinate plane
domain
a set containing the first member of its ordered pair
scatter plot
A graph with points that are plotted to show the relationship between two data sets.
input
A value that is substituted for the independent variable in a function or relation
y = 5
Example of a line with a slope of zero passing through (0,5).
x = -1
Example of a line with no slope passing through (-1,6).
vertical line test
If any vertical line passes through no more than one point of the graph of a relation, then the relation is a function.
y = 6x + 4
Rewrite in slope intercept form: 12x - 2y = -8.
The lines are perpendicular because they have negative reciprocal slopes of 2 and -1/2
Tell whether the lines are parallel or perpendicular: Line 1: through (3,-3) and (-7,2) Line 2: through (-8, 3) and (-6, 7)
x-intercept
The point where the line crosses the x-axix, (x,___)
Domain
The possible values for the input of a relation or function
range
The possible values of the output, or dependent variable, of a relation or function.
output
The result of substituting a value into a function.
slope of perpendicular lines
Two non-vertical lines have slopes that are negative reciprocals of each other.
slope of parallel lines
Two non-vertical lines have the same slope.
f(x) function notation
Used to show that the output value of the function corresponds to the input value (x).
independent variable of a relation or function
What does x represent in an equation?
dependent variable of a relation or function
What does y represent in an equation?
a relation in which each element of the domain is paired with exactly one element of the range
What is a function?
a set of ordered pairs
What is a relation?
y = mx + b
What is slope-intercept form?
y = 3x - 2
What is the equation of a line parallel to the line y = 3x + 1 and passing through (0,-2)?
y = -6x +5
What is the equation of a line passing through (2,-7) and (1, -1)?
y = 2/3 x + 8
What is the equation of a line passing through (3,10) with a slope of 2/3?
y = -3/2 x + 6
What is the equation of a line that is perpendicular to the given line in the graph and passes through the point (4,0)?
(0,0), the point where the x & y axis meet
What is the origin?
m = 7/8
What is the slope between (8,10) and (0,3)?
undefined slope (no slope)
What is the slope for the graph?
0
What is the slope of a horizontal line?
undefined slope
What is the slope of a vertical line?
y = 2x - 4
What is the slope-intercept form of the line in the graph ?
Ax + By = C, where A & B are not equal to zero, traditionally A is positive, and A,B,C are integers.
What is the standard form of a linear equation in algebra?
5x - y = 7
Write the equation in standard form: y = 5x - 7
y = -3x - 4
Write the equation of a line with a slope of -3 and a y-intercept of -4
range
a set containing the second member of its ordered pair
slope
the steepness of a line on a graph, equal to its vertical change divided by its horizontal change
y-intercept
the y-coordinate of the point where the line crosses the y-axis
