Comparing Slope
Cyclist A distance y, in miles, can be represented by the equation
Y = 18x
Where x represents the number of hours the cyclist rides.
Cyclist B distance is shown in the table. __________________________________ x l y
0 l 0
1 l 15
2 l 30
Cyclist A: m = 18
Cyclist B: m = 45/3 = 15
Cyclist A has a greater slope
The distance y in miles that a cyclist travels and the time x in hours are represented by the equation
y - 12x
Find and interpret the slope of the line representing this relationship.
The cyclist travels 12 miles per hour
4x + 7 = 2x + 15
One Solution
3x + 5 > 17
x > 4
You pay a $12 membership fee to join a fitness center. You also pay $5 for each class you attend.
Write an equation in slope-intercept form that represents the total amount of money you pay, y, for attending x classes.
y = 5x + 12
Water tank A contains an amount of water y, in gallons, after x minutes. The amount of water is represented by the equation
Y = 6x + 12
Water tank B amount of water is shown in the table.
__________________________________ x l y
2 l 25
5 l 43
8 l 61
Tank A: m = 6
Tank B: m = 18/3 = 6
The two water tanks have the same slope. Their rates of change are both 6 gallons per minute
The amount of water y in liters used by a machine and the number of minutes x it operates are represented by the equation
y = 2.5x
Find and interpret the slope of the line representing this relationship
Slope = 2.5
The machine uses 2.5 liters of water per minute
5x - 3 = 5x - 3
Infinitely Many Solutions
−4x + 7 ≤ 23
x ≥ −4
A car travels 48 miles every hour at a constant speed.
Write an equation that represents the distance traveled, y, after x hours.
y = 48x
Train A travels at a constant rate of 42 miles per hour. The distance traveled by train B is shown in the table.
__________________________________ x l y
0 l 0
1 l 36
2 l 72
Which train is traveling at a greater rate? How much greater is its slope?
Train A: m= 42
Train B: m = 108/3 = 36
Train A has the greater rate.
The amount of flour y in cups needed to make a recipe and the number of batches x made are represented by the equation
y = 2 1/4x
Find and interpret the slope of the line representing this relationship
Slope = 2 1/4
The recipe requires 2 1/4 cups of flour per batch
4(2x - 3) + x = 3x + 12
One Solution
5x − 8 ≥ 2x + 10
x ≥ 6
A streaming service charges a $9 monthly fee plus $2 for each movie you rent.
Write an equation in slope-intercept form that represents the total amount you pay, y, when you rent x movies.
y = 2x + 9
Hiker A’s Elevation decreases at a rate of 8 meters per minute.
Hiker B’s elevation is represented by the table.
__________________________________ x l y
0 l 0
1 l 36
2 l 72
Which hiker’s elevation is changing at a greater rate? How much greater is the slope?
Hiker B: m = -24/3 = -8
The hikers have the same rate of change.
The temperature y, in degrees Fahrenheit, of a freezer is represented by the equation
y = 3x + 20
Where x represents the number of hours after the freezer is turned on.
Find and interpret the slope of the line representing this relationship. Is this a proportional relationship?
Slope = 3
The temperature increases 3*F per hour
Not proportional because the equation has a y-intercept of 20, so the line does not pass through the origin
3(2x + 4) + 5x = 11x + 12
Infinitely Many Solutions
−3 (2x − 4) < 18
x > −1
A school is ordering notebooks for students. Each notebook costs $3.
Write an equation that represents the total cost, y, for purchasing x notebooks.
y = 3x
The amount of battery remaining on a device A decreases at a rate of 12 percentage points per hour.
The battery percentage of device B is shown in the table. __________________________________ x l y
0 l 0
1 l 36
2 l 72
Compare the slopes of the two relationships. Which device’s battery percentage is decreasing faster?
Device A: m = -12
Device B: m = -18/3 = -6
The first device's batter is decreasing faster.
Where x represents the number of hours the student has been reading
y = -15x + 120
where x represents the number of hours the student has been reading
Find and interpret the slope of the line. Is this a proportional relationship?
Slope = -15
The student reads 15 pages per hour, so the number of pages left decreases by 15 pages each hour
Not proportional because the y-intercept is 120, not 0. The line does not pass through the origin.
Make this have No Solution
____x + ___ = 2(x + 4) + x + 1
Coefficient : 3x
Constant : Anything except 9
7 − 2(x + 3) ≥ 19
x ≤ −3
A plumber charges a $45 service fee plus $30 for every hour of work.
Write an equation in slope-intercept form that represents the total cost, y, for x hours of work.
y = 30x + 45