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Chapter 4.1

Terms in this set (27)

ordered pair
a pair of numbers written within parentheses in which the order of numbers is important.
example: (4, 1) -- the first number is relative to the x-axis, the second number is relative to the y-axis.
origin
common point 0
x-axis
horizontal number line
y-axis
vertical number line
the x-axis and y-axis make up
the rectangular (or Cartersian) coordinate system
plot
to locate
components
the numbers in the ordered pairs; they are the coordinates of the corresponding point
quadrants
four regions of the graph (I, II, III, IV) that are read counterclockwise from the upper-right quadrant
points on the x-axis, y-axis, or origin
do NOT fall in any quadrant
to find ordered pairs that satisfy an equation
1. Select any number for one variable
2. Substitute that number into the equation for that variable
3. Solve for the other variable
since any real number could be selected for one variable and would lead to a real number for the other variable
linear equations in two variables have an infinite number of solutions
the graph of the equation
the set of points corresponding to all ordered pairs that satisfy the equation.
most equations in two variables
are satisfied by an infinite number of ordered pairs, so their graphs include an infinite number of points (these points lie on a straight line)
first-degree equation
no term with a variable to a power greater than one
Example: 2x + 3y = 6
since first-degree equations with two variables have straight line graphs
they are called linear equations in two variables
linear equation in two variables
Ax + By = C, where A, B, and C are real numbers, and A and B are not both 0; this form is called standard form.
x-intercept
the point (if any) where the line intersects the x-axis
y-intercept
the point (if any) where the line intersects the y-axis
the y-value of the point where a line intersects the x-axis is
0
the x-value of the point where a line intersects the y-axis is
0
finding intercepts
Let y = 0 to find the x-intercept
Let x = 0 to find the y-intercept
graphs with vertical lines
y = 2
Since y is always 2, there is no value of x corresponding to y = 0, so the graph has no x-intercept. the y-intercept is (0, 2)
graphs with horizontal lines
x + 1 = 0, or x = -1
Since x is always -1, there is no value of y that makes x = 0, so the graph has no y-intercept. The x-intercept is (-1,0)
to avoid confusing equations of horizontal and vertical lines
1. An equation with only the variable x will always intersect the x-axis and thus will be vertical.
2. An equation with only the variable y will always intersect the y-axis and thus will be horizontal.
some lines
have both the x- and y-intercepts at the origin; the ordered pair (0, 0) passes through the origin.
if the coordinates of the endpoints of a line segment are known
the coordinates of the midpoint can be found
midpoint formula
(x₁+ x₂/2, y₁+ y₂/2)
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