Slope and Rate of change
What is the slope of a line that passes through (2,3) and (4,7)
2
What is the y intercept of the equation y=5x-2
-2
What is slope intercept form
y=mx+b
What is the constant of proportionality in this table
x: 1 2 3
y: 3 6 9
3
A phone plan cost $25 per month plus $0.10 per text. Write an equation
y=0.10x+25
A car travels 120 miles in 3 hours. What is the unit rate?
40 miles per hour
How do you find the slope of a line from a graph?
Choose two points and use rise/run
Write an equation for a line with a slope of 4 and a y-intercept of-7
y=4x-7
Does the equation y=4x+1 represent a proportional relationship?
No because it has a y intercept of 1, not 0.
A car rental cost $20 per day plus $0.15 per mile. What is the total cost for renting for 3 days and driving 100 miles.
$63
Explain what a negative slope could represent in a real world situation
A negative slope represents a decreasing trend, such as losing money or descending a hill.
If a line passes through (0,5) and has a slope of -3, write its equation.
y=-3x+5
Convert the equation 2x+3y=12 to slope intercept form.
y=-2/3x+4
A table shows a linear relationship with a slope of -5. Write a possible equation for the relationship.
y=-5x+b
A plumber charges a $50 base fee and $30 per hour. Compare his cost to plumber b who charges a $70 base fee and $25 per hour.
The first plumber is cheaper after a certain number of hours
If a line has a slope of 0, what does that mean about the line?
The line is horizontal
A line has a y-intercept of -4 and passes through (2,2). Write its equation.
y=3x-4
The cost of a gym membership is a $30 sign up fee plus $10 per month. Write an equation for the total cost y after x months.
y=10x+30
Two different graphs show the equations y=3x+4 and y=3x-2. What is the difference between these lines?
The y intercepts are different
A hiker is descending a mountain at a rate of 200 feet per hour. Write an equation an equation for their altitude after x hours.
y=-200x+b where b is the starting altitude
Find the slope of the given equation 3x-2y=8
slope = 3/2
A student says the equation y=2x+1 and the graph below don't match. What mistake have they made?
they may have misidentified the slope or y-intercept
A taxi charges a $5 base fare plus $0.50 per mile. What does the slope represent in this situation.
The slope 0.50 represents the cost per mile
Describe one advantage of using a table vs a graph to compare linear relationships.
A table shows exact values, while a graph is a visual trend.
The equation y=-2x+50 represents the amount of water in the tank after x hours. What does the slope mean in context?
The water level decreases by 2 gallons per hour