Graphs
Slope
Equation of a line
y-intercept
100
Which graph does not show a linear function?
Graph 4
100
What two formulas used to calculate slope?
m = (rise)/(run)
m = (triangle y)/(triangle x)
100
In slope intercept form y=mx+b what does the variable m represent? What does the variable b represent?
m = slope
b = y-intercept
100
Describe how to find the y-intercept when analyzing a graph.
Describe how to find the y-intercept when analyzing a data table?
On a graph, the y-intercept is where a line crosses the y- axis.
When looking at a table or set of ordered pairs the y-intercept is the value of y when x=0.
200
Who was traveling at a faster speed? How do you know?
Pennington, because his slope is greater.
200
1. A positive slope show an (increase/decrease/remains constant) in the y-value as the x value increases.
2. A Negative slope show an (increase/decrease/remains constant) in the y-value as the x value increases.
3. A line with zero slope shows an (increase/decrease/remains constant) in the y value as x increases.
Increase
Decrease
Remains Constant
200
A line can be represented by the equation y = -3x + 9
Use the equation of the line to complete the ordered pairs below.
(16,___) (___,27) (4.5,___)
(16,-39) (-6,27) (4.5,-4.5)
200
Which line has the greatest y-intercept?
Red line
300
What is the slope of this line?
m=1/2
300
Describe what a slope is in your own words.
It is the rate of change...
300
A kite is 160 feet in the air when the flyer starts to wind it down. After 24 seconds the kite is 64 feet in the air. Write the equation in slope intercept form that shows the relationship between the kites height (y) and the amount of time in seconds they have been winding it down. Then write a sentence that explains your equation.
y = -4x + 160
The kites height is equal to -4 times the number of seconds, because they are winding the kite down 4 feet every second. Then add 160 because this is the height the kite started at.
300
The cost for copies at Paper Depot can be represented by the equation y = .10x + 5 where y is the cost and x is the number of copies. The graph below shows the cost at Carl's Color Copies . Who charges a smaller flat fee? How do you know?
Carl's Color Copies charges a smaller one time fee because it has a y-intercept of 2 which is less than the y-intercept of Paper Depot.
400
Write an equation for the line in slope intercept form.
y= -2/3x + 5
400
Calculate the slope of a line that intersects the points (-4,4) and (8,8).
m = 1/3
400
A parking garage charges a flat fee and then an hourly rate. On Monday you park your car for 6 hours and get charged $23.50. On Tuesday you park your car for 10 hours and get charged $32.50. What is the flat fee? How much is the hourly charge? What is the equation that represents this linear function?
y=2.25x + 10
$2.25 per hour parked
$10 flat fee
400
A car shipping service charges a flat fee and then an additional fee per mile the car is shipped. The equation y = 0.75x + 125 where y is the total cost and x is the number of miles shipped.
What is the y intercept? What does the y-intercept mean?
The y intercept is 125 and it is the flat fee the company charges.
500
Create a graph for the following scenario. Then write the equation for the line in slope intercept form.
A D.J. charges a flat rate of $250 and an additional hourly fee of 35$ per hour.
Y = 35x + 250
Graph should have a slope of 25 and a y-intercept of 250.
500
Mia started a hike at mile marker 15 and after 4 hours was at mile marker 25. Charlie started at mile marker 3 and after 6 hours was at mile marker 19. Who was hiking at a faster rate? How much faster?
Charlie was hiking 1/6 miles per hour faster
Mia -
2 1/2 mph
Charlie -
2 2/3 mph
500
You are comparing rates to determine which phone company will cost the least. V-mobile charges a flat fee of $10 and an extra $15 per gigabyte of data. Torizon charges a flat fee of $40 and an extra $5 per gigabyte. Write an equation in slope intercept form for both companies. Then use the equation to determine the cost of a 6 Gigabyte plan for both companies
V-Mobile - y=15x+10
6 GB plan = $100
Torizon - y = 5x + 40
6 GB plan = $70
500
An elevator ascends and descends at a constant rate. After 10 seconds the elevator is on the 12th floor. After 18 seconds the elevator is on the 8th floor. What is the y-intercept and what does it represent?
The y-intercept is 17
She started on the 17th floor of the building.