Transcript Unit 4 PowerPoint

ALGEBRA UNIT 4: GRAPHS OF
EQUATIONS AND FUNCTIONS
Unit 4 PowerPoint
THE COORDINATE PLANE
THE COORDINATE PLANE REVIEW
Overview
4 quadrants
Labeled with x and y axis
 X axis is horizontal
 Y axis is vertical
Labeled with coordinates (x, y)
LABELING POINTS
Label the points
(4, 3)
(-1, 0)
(-2, - 3)
(2, - 3)
HIDDEN MESSAGE ACTIVITY
Complete the coordinate plane activity to reveal
the secret message.
GRAPHS OF LINEAR EQUATIONS
GENERAL GRAPH OF A LINEAR FUNCTION
When you hear linear, what do you think of?
What do you think a linear function will look like?
GRAPHING A LINEAR EQUATION
A taxi fare costs more the further you travel. Taxi’s charge
a fee on top of the per-mile charge to cover hire of the
vehicle. For our example, the taxi charges a set fee of $3,
plus $.80 per mile traveled. Write an equation and graph
the solutions.
GRAPHING A LINEAR EQUATION
Equation: y = $3.00 + $.80x
 Where y is total cost and x is miles traveled.
Graph:
 1- make a t-chart
 2- pick x- values to plug in
 3- calculate the y- values
 4- plot the points
 5- draw the line
GRAPHING A LINEAR EQUATION
A small business has a debt of $500,000 incurred from
start-up costs. It predicts that it can pay off the debt at a
rate of $85,000 per year according to the equation
governing years in business (X) and debt measure in
thousands of dollars (y).
Y = -85x + 500
Graph the equation and use the graph to predict when the debt
will be fully paid.
GRAPHING A LINEAR EQUATION
Graph:
Y = 3x + 2
Y = - 4x + 5
Y = .5x – 1.5
GRAPHS OF HORIZONTAL AND VERTICAL LINES
How would you graph the two following lines?
Y = 3
X = - 4
HORIZONTAL AND VERTICAL LINES
“Mad-cabs” have an unusual offer
going on. They are charging $7.50 for
a taxi ride of any length within the city
limits. Graph the function that relates
the cost of hiring the taxi (y) to the
length of the journey in miles (x).
USING AND INTERPRETING LINEAR GRAPHS
Use the graph to convert:
70 F to C
0 F to C
30 C to F
0 C to F
ACTIVITY
Grab a laptop and go to this website:
http://www.mathplayground.com/SaveTheZogs/SaveTheZogs.htm
l
You are going to save the zogs using your equation tools. See
what level you can get too.
GRAPHING USING EQUATIONS
WHAT IS A LINEAR FUNCTION?
How many times will the line cross the x-axis? What about
the y-axis?
X- AND Y- INTERCEPTS
X-intercept: where the line touches/crosses the x axis
(where the y value will be zero.)
Y-intercept: where the line touches/crosses the y axis
(where the x value will be zero.)
SLOPE- INTERCEPT FORM OF AN EQUATION
SLOPE-INTERCEPT FORM OF AN EQUATION
Y = mx + b
Where x and y are your coordinate points
M is your slope
B is your y-intercept (where the line touches the y-axis)
SLOPE-INTERCEPT FORM
What is the slope, what is the y-intercept?
Y = 5x + 3
Y = -12x – 4
Y = x + 1.5
SLOPE- INTERCEPT FORM
To find slope: calculate the rise and run of a line
FINDING SLOPE FROM A GRAPH
Find the rise and the run, then divide the two (Rise / Run)
Example:
SLOPES OF HORIZONTAL AND VERTICAL LINES
DETERMINING SLOPE GIVEN TWO POINTS ON A
LINE
Given two points (x1, y1) and (x2, y2)
𝑠𝑙𝑜𝑝𝑒 =
𝑦2 −𝑦1
𝑥2 −𝑥1
FINDING SLOPE GIVEN TWO POINTS
Given the points:
(19, -16) and (-7, -15)
(-4, 7) and (-6, -4)
LINEAR FUNCTIONS IN REAL-LIFE
WHAT IS THE IMPORTANCE?
What would be the importance of the y- intercept in the
example below:
A taxi fare costs more the further you travel. Taxi’s
charge a fee on top of the per-mile charge to cover hire
of the vehicle. For our example, the taxi charges a set fee
of $3, plus $.80 per mile traveled. Write an equation
and graph the solutions.
WHAT IS THE IMPORTANCE?
Farmer Ali had a well on his property 200 feet deep.
When the well went dry, he hired a company to drill the
well deeper. He used the equation d= -75t – 200 to find
the depth of the well, d, using the number of days the
company drilled, t.
What is the slope of the line?
What does the slope represent in the context of the problem?
WHAT IS THE IMPORTANCE?
Pierce the plumber charges $25 for a service call. He uses
the equation C = 50h + 25 to determine the charge of his
services, C, after working h hours.
What is the slope of the line?
What does the slope represent in the context of the problem?
What is the y-intercept of the line?
What does the y-intercept represent in the context of the
problem?
FINDING INTERCEPTS IN SLOPE INTERCEPT FORM
To find intercepts in slope intercept form:
Plug in 0 for x to find the y-intercept
Plug in 0 for y to find the x-intercept
GRAPHING INTERCEPTS IN SLOPE INTERCEPT
FORM
Once you have determined the intercepts of the graph,
plot them and draw a line between the two.
EXAMPLE
Y = 2x – 3
STANDARD FORM OF AN EQUATION
FINDING INTERCEPTS IN STANDARD FORM
To find intercepts in standard form,
Plug in 0 for x to find the y-intercept
Plug in 0 for y to find the x-intercept
GRAPHING INTERCEPTS IN STANDARD FORM
Once you have determine the intercepts of the graph, plot
them and draw a line between the two.
EXAMPLE
4x – 3y = 12
GRAPHING PRACTICE WORKSHEET