Functions
What is the slope Formula?
y = mx + b
A line rises 3 units and runs 3 units. What is the slope?
m= 1
A student says the slope of a line that goes up 4 and right 2 is 2/4.
What is the mistake?
They flipped the fraction
(Correct slope: 4/2=2)
A gym charges a $25 sign-up fee and $15 per month.
- Part A: Write an equation to represent the total cost after x months.
- Part B: What does the $25 represent in the situation?
A: y=15x+25
B: The $25 is the starting cost (y-intercept)
A student earns $12 per hour and starts with $20. Write an equation for total money y after x hours.
y=12x+20
What is the slope and y intersect of y = 5/8x +9
m = 5/8
b = 9
A line goes up 4 but moves left 2. What is the slope?
m=-2
A student says:
The equation y = 4x has a y-intercept of 4.
What is the error?
They confused slope with y - intercept.
Slope = 4
y-intercept = 0
A student is tracking how many pages they read each day: x = Days, y = pages
(1,12), (2,24), (3,36),(4,48)
Write an equation to model the situation.
y=12x
A taxi charges $3 to start plus $2 per mile. Write an equation for total cost yyy.
y=2x+3
What is the equation of a line with slope 3 and y-intercept 4?
y=3x+4
A graph shows a horizontal line passing through y = 6. What is the slope?
m = 0
A line goes down 3 and right 1.
A student says the slope is 3.
They forgot the negative sign
(Correct slope: m = −3)
Two streaming services charge as follows:
Service A: $12 per month
Service B: $5 per month + $2 per movie watched
Part A: Write equations for both plans.
Service A: y = 12
Service B: y = 2x+5
.
A delivery service charges $5 for every package plus a $10 delivery fee.
Write an equation for the total cost y.
y=5x+10
What is the equation of a line with slope 2 that passes through (1, 5)?
y=2x+3
Given y = 3x+5, graph this equation when x = -1,0,1
Points: (-1, 2) ,(0,5), (1,8)
A line has a slope of 3 and crosses the y-axis at −2.
A student writes: y=−2x+3 y
What is the mistake?
They switched the slope and y-intercept
(Correct: y=3x−2)
Two ride plans: Plan A: $3 base fee + $2 per mile, and Plan B: $8 base fee + $1 per mile
A: Write both equations.
B: When do they cost the same?
A) Plan A: y = 2x+3
Plan B: x+8
B) x = 5
Problem: A tank has 50 gallons and loses 5 gallons per hour.
A: Write an equation.
B: What does the slope mean?
A: y=−5x+50
B: The water decreases by 5 gallons per hour
A line passes through the points (2, 7) and (6, 15). What is the equation of the line?
y=2x+3
Graph using points (0,7), (2,11), (4,15):
1) Graph
2) Find the equation of the line
1) Graph: Teacher inspect
2) y=2x+7
A line passes through (0, 3) and (2, 7).
A student says the slope is 2 because “the y-values increase by 2.”
What is the mistake?
They only looked at the change in y-values and ignored the change in x-values.
(Correct slope: m = 2, but the reasoning must include both rise and run)
A water tank starts with 100 gallons and drains at a rate of 8 gallons per hour.
Part A: Write an equation to model the amount of water after 𝑥 x hours.
Part B: How much water is left after 6 hours?
Part C: What does the slope represent in this context?
A: 𝑦 = − 8 𝑥 + 100 y=−8x+100
B: 𝑦 = − 8 ( 6 ) + 100 = 52 gallons
C: The slope (-8) represents water decreasing by 8 gallons per hour
A situation is modeled by:
y=3x+7
A student says:
“The 7 means the cost increases by 7 every time.”
What is the error in the student’s thinking?
The 7 is the starting value (fixed amount), not the rate of increase.
The rate of increase is 3.
👉 (Tests understanding of slope vs y-intercept in context)