SLOPE & Y-INTERCEPT
Find a slope when 2 ordered pairs
1) (2,6), (-3,4)
2/5
Finding the constant rate of change:
(-3,5) (5,-1)
-3/4
Determine if it is a linear function. If it is, state the constant rate of change
y = -3x+5x3
NOT A LINEAR FUNCTION
Linear functions always have a ---------------- ---------.
CONSTANT RATE OF CHANGE
Identify slope and y-intercept of a function:
5y= -10x -3
m= -2
b= -3/5
a slope intercept form
y = mx + b
We can easily tell just by looking at a graph whether it is a function or not by using a -------- ---- ----.
vertical line test
Finding the constant rate of change:
Adelynn made 100 necklaces and gave away 3 per week
-3
Finding the constant rate of change:
Y = -3 + 1.5x
1.5
Tony’s Aunt agrees to give Tony $400 to buy a used car as long as Tony pays back $40 per month. What is our equation?
y=40x-400
Indicate whether or not it is a linear function. If it is, find the slope, y-intercept, and constant rate of change
2x – 5x + 3y = –2
yes. slope 1. y-intercept -2/3. constant rate 1
Read the scenario and determine if it is a linear function. Show equations and constant rate of change.
Equation: y = .05x + 2
Constant rate of change: 0.05
This is a linear function
Determine if it is a linear function just by looking at the equation:
y = 0.25 + 0.5 (x – 2)
Yes. It is a linear function. The constant rate of change is 0.5
SLOPE-INTERCEPT FORM: ----------
where m, is the ------- also know as the --------- ------ ----------
and b, is the ----------, the initial value.
y=mx+b
m: slope AKA rate of change
b:y-intercept
Identify slope and y-intercept of a function:
4x + y = -7
m= - 4
b= - 7
Indicate whether or not it is a linear function. If it is, find the slope, y-intercept, and constant rate of change.
(–1/2)x + 3y = 10
yes. slope 1/6. y-intercept 10/3. constant rate of change 1/6.
Determine if it is a linear function. If it is, state the constant rate of change
A. y= (1/3)x - 2/5
B. 3x4+9x = 4 + y
A. YES. 1/3
B. NOT A LINEAR FUNCTION
Write an equation for each contextual situation. Indicate the rate of change (slope) and the y-intercept:
Andy has $1500 in his bank account. Each month, he deposits $300.
y = 300x + 1500; rate of change = 300; y-intercept = 1500
Write an equation for each contextual situation. Indicate the rate of change (slope) and the y-intercept:
Sam rents a bike for a fixed price of $25 but has to pay additional $5 per hour.
y = 5x + 25; rate of change = 5; y-intercept = 25
Write an equation for each contextual situation. Indicate the rate of change (slope) and the y-intercept:
Tom borrowed $400 from his friend, Scott. He made an arrangement to pay him back $25 per week.
y = 25x – 400; rate of change = 25; y-intercept = –400
Kayla plans to use 60 inches of wire to build a rectangle that is seven times as long as it is wide. What will be the area of her rectangle?
98.4375 square inches.
Jessica is taking a test that has 30 questions. She earns 9 points for every correct answer and loses 5 points for every wrong answer. If Jessica’s score is 18, how many questions did she answer correctly on the test?
X = 12
A lobster’s age in years is approximately his weight multiplied by 4, plus 3 years. Write this rule of thumb as a linear equation and determine the age of a 5–pound lobster. How much will a 15 year old lobster weigh?
W= 3
Create an equation and table by using a contextual situation. For the table, use 0, 1, 2, 3 for the x values.
Leah borrowed $300 from her mom. She decided to pay her back $20 per week.
y = 20x – 300
For the table: x values: 0, 1, 2, 3 and y values are –300, –280, –260, –240]
On a blueprint for Monica’s house, the length of the living room is 5 inches. The scale on the blueprint is 1 /4 in = 1 foot. What is the actual length of Monica’s living room?
20 FEET