Download Math 142–Rodriguez Lehmann–1.2

Math 142–Rodriguez
Lehmann–1.2
Graphing Linear Equations
A. Solutions to equations
a. Ordered pairs are written as (x,y) where x is the independent variable and y is the
dependent variable.
b. An ordered pair (a,b) is a ____________ of an equation if the values a and b
make the equation a true statement.
(2,3) is a solution to x+y=5
c. We say that (2,3) _______________ the equation.
d. The _______________ _____ of an equation is the set of all solutions to the
equation.
e. Solutions can be plotted on a coordinate system.
Example: Find solutions to x + y = 5. Plot them.
B. Graph a linear equation
a. The graph of an equation in two variables is a visual way to represent _____ the
_______________ of the equation.
b. If an equation can be put into the form y=mx+b, where m and b are constants
(numbers), then the graph of the equation is a __________.
Graph the equation by hand. Verify your graph using ZStandard followed by ZSquare
on a graphing calculator.
Example 1:
1
y=− x+2
3
c.
Example 2:
2( y − 3 ) = 4( x + 1 )
Example 3:
−x + 2 y = 6
What about equations that look like x= # and y = #?
Example: Find points that satisfy x=2. Plot them.
The graph of x = # is a ____________________ line.
The graph of y = # is a _____________________ line.
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Example 4: Graph y=–2.
Example 5: Find an equation of the line sketched.
y
y
x
x
d. Recap: If the equation can be put into the form y=mx+b or x=a, where m, b, and a
are constants (numbers), then its graph is a line. These are called ____________
equations in two variables.
e. Recap: The graph is a visual to represent the solutions to the equation.
Which points represent ordered pairs that satisfy the equation?
C. Find and interpret intercepts
a. The x-intercept is the point where the graph intersects the x-axis.
(
,
)
To find it: let ___________ and solve for ___.
b. The y-intercept is the point where the graph intersects the y-axis.
(
,
)
To find it: let ___________ and solve for ___.
y
x
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Find all x-intercepts and y-intercepts.
Example 1: 4x – 6y = –12
Example 2:
Example 3: y = 3x – 6
Example 4: x = 2
y=–3
c. When graphing equations we can find the intercepts instead of finding random points.
d. Interpreting Intercepts
Example 6: A person lowers their hot-air balloon by gradually releasing air from it. Let
x be the number of minutes that he has been releasing the air from the balloon, and
let y be the altitude of the balloon (in feet). Assume the relationship between x and y
is described by the equation y=–150x+750.
a. Graph the equation by hand.
b. Find the y-intercept. What does it mean in this situation?
c. Find the x-intercept. What does it mean in this situation?
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