Download Y = -3x + 2

Linear
Functions
Slope
Parallel &
Perpendicular
Lines
Different
Forms of
Linear Equations
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Graphing
Linear Inequalities
and Systems
Misc. Linear
Functions
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$100 Question Linear Functions
Explain how you know if a graph
represents a linear function
$100 Answer Linear Functions
A graph represents a linear function
if it is a straight line
**vertical lines are linear but not functions (fails vertical line test.)
$200 Question Linear Functions
Which table(s) are linear?
Explain how you know.
A.
B.
$200 Answer Linear Functions
B.) x and y are both going up
with constant rates
* same rate of change *
Rate of change = change of y
change of x
x is not a constant change in table A
$300 Question Linear Functions
Make a table and graph for y = -x + 3
Is this equation linear? Explain.
$300 Answer Linear Functions
Graph has a negative slope—straight line
It is a linear function
because table has a
constant rate of change
and graph is a straight
line
$400 Question Linear Functions
Let y = 2x + 9. If the value of x increases
by 6, which of the following best describes
the change in the value of y.
a.) decreases by 6
b.) increases by 6
c.) increases by 12
d.) increases by 21
$400 Answer Linear Functions
As x goes up by 6
The value of y. c.) increases by 12
$500 Question Linear Functions
Which of the following equations is not linear?
Explain or show how you know.
A) y = 2x2 – 7
B) -6 = y
C) 4x – 2y = 10
D) y = 3x + 1
$500 Answer Linear Functions
A) y = 2x2 – 7 not linear--exponent
B) -6 = y
horizontal—straight line
C) 4x – 2y = 10 standard form x and y-int. --line
D) y = 3x + 1 slope-int.—always form a line
$100 Question Slope
Find the slope of the line
(0, 4)
(3, -5)
$100 Answer Slope
Rise
Run
m = -3
$200 Question Slope
Write the equation of the line that passes
through each pair of points in slopeintercept form
(-1, 5) and (2, -4)
$200 Answer Slope
1.) Find Slope m = -3
2. ) Choose a point (-1,5)
Use point-slope form then
solve for y
Y = -3x + 2
$300 Question Slope
Put the following equation into slopeintercept form. Identify the slope and yintercept. Then use the slope and y-int. to
graph the line.
3x – y = 2
$300 Answer Slope
3x – y = 2
-3x
-3x
-y = -3x + 2
-1 -1 -1
y = 3x -2 m = 3
b = -2
$400 Question Slope
Laurel graphed the equation
y = -2x + 5. Katelyn then graphed an
equation that was a line that was not as
steep as Laurel’s. Which equation could
have been the one Katelyn graphed?
a.) y = -3x + 5
b.) y = 1/2x + 6
c.) y = 4x – 2
d.) y = -2x + 3
$400 Answer Slope
B.) y = 1/2x + 6 is not as steep.
Fractions (between -1 and 1: non-improper)
are less steep than any integer—
even if it’s negative.
$500 Question Slope
The cost of hiring Zach as a painter is
given by the linear equation C = 10t + 100,
where t is the number of hours Zach
works. Identify the slope and y-int.
What does the slope of the line represent?
What does the y-intercept represent?
$500 Answer Slope
m = 10 The slope means Zach earns $10
per hour.
b = 100 The y-intercept represents base
charge of hiring Zach (when he’s
worked 0 hours, we’d still have
to pay him $100
$100 Question Parallel &
Perpendicular Lines
What are two different ways that lines can
be perpendicular?
$100 Answer Parallel &
Perpendicular Lines
Vertical lines are perpendicular to a
horizontal lines. Ex. x = 3 and y = -2
When the product of slopes = -1 (or are
negative reciprocals of each other)
Ex. 4 and -1/4
$200 Question Parallel &
Perpendicular Lines
A line has the equation x + 2y = 5
What is the slope of a line parallel to this
line?
a.) – 2 b.) - ½ c.) ½
d.) 2
$200 Answer Parallel &
Perpendicular Lines
A line has the equation x + 2y = 5
1. Put line in slope-int. form y = -1x + 5
2
2
2. Parallel -- same slope -- b.) - ½
$300 Question Parallel &
Perpendicular Lines
$300 Answer Parallel &
Perpendicular Lines
A. 1 and -1 are “opposite reciprocals”
$400 Question Parallel &
Perpendicular Lines
$400 Answer Parallel &
Perpendicular Lines
Line AB has a slope of 1 and Line BC
has a slope of -3/2 and Line AC has a
slope of 0. None of the slopes will
have a product of -1 (are negative
reciprocals) so D is the answer
$500 Question Parallel &
Perpendicular Lines
Write an equation that is perpendicular
to the given line below that passes
through the point (- 6, 2)
$500 Answer Parallel &
Perpendicular Lines
1. Slope will be -3 (opp. reciprocal)
2. Use point-slope form
y- 2 = -3(x – (-6)) Distributive Prop.
y = -3x -16
$100 Question Different Forms
of Linear Equations
Find and use the x and y intercepts to
graph the line.
-x + 3y = 6
$100 Answer Different Forms of
Linear Equations
-x + 3y = 6
-x + 3y = 6
0 + 3y = 6
-x + 3(0) = 6
y-int. = 2
-x = 6
(0,2)
x-int. = -6
(-6,0)
(0,2)
(-6,0)
$200 Question Different Forms
of Linear Equations
Find and use the x and y intercepts to
graph the line.
-2x = 12 + 4y
$200 Answer Different Forms of Linear Equations
-2x = 12 + 4y
-4y from both sides
-2x - 4y = 12
Now in standard form
x-int. = (-6,0)
y-int. = (0,-3)
(-6,0)
(0, -3)
$300 Question Different Forms
of Linear Equations
What is the x-intercept of the linear
function f(x) = -3x + 6?
Note: f(x) is another way to write ‘y’
a.) -2
b.) 2
c.) 3
d.) 6
$300 Answer Different Forms of
Linear Equations
f(x) = -3x + 6 Think: y = -3x + 6
add 3x to both sides –standard form
y + 3x = 6
0 + 3x = 6
x-int. = 2 (b)
$400 Question Different Forms
of Linear Equations
A line has a slope of 2/3 and passes
through the point (-3, 4).
What is the equation of the line in
point-slope form?
What is the equation of the line in
slope-intercept form?
$400 Answer Different Forms of
Linear Equations
Point-slope form
y- 4 = 2/3[x – (-3)]
y – 4 = 2/3(x + 3)
Slope-Intercept Form y = 2/3x + 6
$500 Question Different Forms
of Linear Equations
Is every linear relationship a direct
variation? Is every direct variation a linear
relationship? Explain.
$500 Answer Different Forms of
Linear Equations
Every linear relationship is not a direct
variation—only if the y-int. is 0. However,
every direct variation is linear because it has a
constant rate of change.
Direct Variation: y = 3x (also linear)
Not a direct variation y = 3x +5 (is linear)
$100 Question Graphing Linear
Inequalities and Systems of Equations
Graph each inequality
y > -3x + 2
$100 Answer Graphing Linear
Inequalities and Systems of Equations
m = -3 b = 2
Dashed
(0,0) not a solution
$200 Question Graphing Linear
Inequalities and Systems of Equations
Graph each inequality
4x + y ≤ 1
$200 Answer Graphing Linear
Inequalities and Systems of Equations
Solve for y
m = -4 b = 1
Solid Line
(0,0) is a solution
$300 Question Graphing Linear
Inequalities and Systems of Equations
Solve the system by graphing
2y = 8
3y = 2x + 6
$300 Answer Graphing Linear
Inequalities and Systems of Equations
$400 Question Graphing Linear
Inequalities and Systems of Equations
Solve the system by graphing
y – 1 = 2x
-y = -2x -1
$400 Answer Graphing Linear Inequalities
and Systems of Equations
$500 Question Graphing Linear
Inequalities and Systems of Equations
$500 Answer Graphing Linear
Inequalities and Systems of Equations
Find x and yintercepts to graph
Solid Line
(0,0) is a solution
$100 Question Miscellaneous
The table shows an employee’s pay per hour.
Determine if there is a direction variation
between the pay and number of hours worked.
If so, find the equation of direct variation
$100 Answer Miscellaneous
You can use the ratio
to check.
17/2 = 8.5 and 34/4 = 8.5 ratios are =
(proportional) so it’s a direct variation
The equation would be y = 8.5x
$200 Question Miscellaneous
Solve the system by substitution
x = 2y + 6
y = -3x + 4
$200 Answer Miscellaneous
Could have also
substituted top
equation into the
bottom.
$300 Question Miscellaneous
Solve the system of equations
x–y=4
x – 2y = 10
$300 Answer Miscellaneous
Could have used
other ways to
eliminate or you
could have used
the substitution or
graphing methods
Remember to check your answer by
substituting solution into each original
equation.
$400 Question Miscellaneous
$400 Answer Miscellaneous
$500 Question Miscellaneous
Solve the system of equations by elimination
$500 Answer Miscellaneous
Could have also
eliminated the y’s
Remember to check
your answer by
substituting solution into
each original equation.