Slope and Rate of Change
What is another way to say rate of change?
Slope
What is another way to say initial value?
The y-intercept
A taxi company charges $3.00 per mile plus a $2.50 flat fee. What is the initial value?
$2.50 (flat fee)
True or False
In a linear function, the rate of change is always constant
True
Find the slope of the line represented by the equation y=−(3/4)x+7
The slope is - (3/4)
In the equation y=mx+b, what does the letter b represent?
The y-intercept (initial value)
A cell phone plan costs $20 per month plus $0.10 per text. Write an equation to represent the total cost of this linear function
y=0.10x+20
A linear function is represented by what equation?
y= mx+b
What is the formula for finding the slope between two points (x1,y1) and (x2,y2)
m = (y2- y1)/ (x2- x1)
What is the y-intercept of the equation y=3x−5?
The y-intercept is -5
If a bathtub fills at a rate of 5 gallons per minute and already contains 10 gallons of water, which statement correctly describes the rate of change?
A) The initial amount of water is 5 gallons
B) The rate of change is 10 gallons per minute
C) The rate of change is 5 gallons per minute
D) The total water after 3 minutes is 10 gallons
C) The rate of change is 5 gallons per minute
The y= intercept or initial value is the value of y when x = _____
zero
Find the slope of the line that passes through the points (2, 3) and (5, 9)
slope = 2
Find the initial value of the function represented by the table:
x: 0, 1, 2, 3
y: 6, 10, 14, 18
The initial value is 6
A gym membership costs $25 per month plus a one-time initiation fee of $50. What does the rate of change represent in this scenario?
A) The $50 initiation fee
B) The $25 monthly fee
C) The total cost after 6 months
D) The number of months in the membership
B) The $25 monthly fee
The y-intercept is the point where the line crosses the____ axis . At this point, the ___ coordinate is always zero.
crosses the y-axis, therefore the X coordinate is always zero
A line passes through the points (-2, 4) and (3, -6). What is the slope of the line?
Slope = -2
A line has a slope of 4 and passes through the point (0, 2). What is the equation of the line?
y=4x+2
A runner starts a race at a pace of 6 miles per hour. After 2 hours, she has run 12 miles. What is the initial distance she started at? (Assume the relationship is linear.)
Initial distance = 0 miles (she started at the starting line)
What does the word "linear" mean in Latin?
"Linea" — meaning line