Transcript Review

Chapter 7
Graphing Linear Equations
REVIEW
Section 7.1
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Cartesian Coordinate System is formed by two axes drawn
perpendicular to each other.
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Origin is the points of intersection for the x- and y-axis (0, 0)
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Horizontal axis is the x-axis
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Vertical axis is the y-axis
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Ordered Pairs are of the form of (x, y)
Section 7.1
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Linear Equations in two variables is an equation that can be
put in the form ax2 + bx = c where a, b and c are real
numbers. Also called standard form
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A Graph of an equation is in two variables is an illustration
of a set of points whose coordinates satisfy the equation
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Collinear points are point that lie in a straight line
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Non-collinear points are not on the line
Section 7.2
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Graphing Linear Equations by Plotting Points
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Solve the linear equation for y
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Select a value for x and substitute in the equations to find a value for y
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Select two additional values for x and find two additional values for y
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Plot the three ordered pairs

Draw a straight line with arrows on the ends through the three points
Section 7.2
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x-intercept is the point where the graph crosses the x-axis
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y-intercept is the point where the graph crosses the y-axis
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Horizontal Line
 Graph is in the form of y = b
 y-intercept is (0, b)
 Slope is 0
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Vertical Line
 Graph is in the form of x = a
 x-intercept is (a, 0)
 Slope is undefined
Section 7.2
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Graphing Linear Equations using x- and y-intercept

Find y-intercept by setting x equal to 0
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Find x-intercept by setting y equal to 0
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Determine a checkpoint with a non-zero value for x and find
the corresponding y
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Plot the x- and y-intercept and the checkpoint
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Draw a straight line with arrows on the ends through the three
points
Section 7.3
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Slope of the Line is the ratio of the vertical change to the
horizontal change between two selected points on the line.
y2  y1 y
vertical change (y)
slope =


horizontal change (x) x2  x1 x
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Positive Slope is a straight line where the value of y
increases as x increases.
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Negative Slope is a straight line where the value of y
decreases as x increases.
Section 7.3
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Parallel Lines – two nonvertical lines with the same slope
and different y-intercepts
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Any two vertical lines are parallel
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Perpendicular Lines – two lines whose slopes are negative
reciprocals of each other
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Any vertical line is perpendicular to any horizontal line
Section 7.4
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Slope-intercept Form of a linear equation
y = mx + b
where m is the slope, and (0, y) is the y-intercept of the line
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To graph ac + by = c, write the equation in slope-intercept
form by solving the equation for y. Then use the slope and
y-intercept to sketch the graph.
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Point-Slope Form of a linear equation
y – y1 = m(x – x1)
where m is the slope of the line and (x1 , y1) is a point on
the line.
Section 7.5
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Linear inequality occurs when the equal sign in a linear
equation is replaced with an inequality sign
<
> ≤ ≥
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To graph in Linear Inequality in Two Variables
1.
2.
3.
Replace the inequality with an equal sign
Draw a graph of the equation.
If symbol is ≥ or ≤ draw a solid line
If symbol is > or < draw a dotted line
Select a point not on line.
If solution shade the region
If not a solution shade the side not containing the points
Section 7.6
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Relation is any set of ordered pairs
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Function is a set of ordered pairs in which each first component
corresponds to exactly one second component
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Domain of a relation or function is the set of first components in
the set of ordered pairs
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Range of a relation or function is the set of second components
on the set of ordered pairs
Section 7.6
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Vertical Line Test
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A vertical line can be drawn through any part of a graph and the
vertical line intersects another part of the graph. The graph is not a
function
A vertical line cannot be drawn to intersect the graph at more than
one point. The graph is a function
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Function Notation is f(x)
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y = mx + b
is a linear equation
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f(x) = mx + b
is a linear function