SME
Grade 8 Math · Problem type
Slope as a unit rate
Use this for “Ana bikes 3 miles in 0.25 hours at a constant speed. What is her speed, and how far in 2 hours?”
Chart
y = 12x
The line goes through (0, 0) and (1, 12).
x = 0.25 h
y = 3 mi
m = 12 mph
This is an example. Type your own values to start a new problem.
m (mph)
=
y (mi)
÷
x (h)
d (mi)
=
m (mph)
×
t (h)
Formulas
m
=
y
÷
x
(unit
rate
=
distance
÷
time)
12 = 3 ÷ 0.25
d
=
m
×
t
(distance
then
=
unit
rate
×
other
time)
24 = 12 × 2
Assumptions
•
A constant speed makes a straight line through (0, 0): a proportional relationship.
•
Its slope is the unit rate: the distance for 1 hour.
•
Any other time: multiply it by the unit rate.
Step-by-step
WE KNOW
x = 0.25 h (time), y = 3 mi (distance), t = 2 h (other time)
FIND
unit rate (m), distance then (d)
Step 1 · Find unit rate (m)
Use m = y ÷ x (unit rate = distance ÷ time)
The slope: the distance for each 1 hour.
m
=
3
0.25
m
=
12
mph
Step 2 · Find distance then (d)
Use d = m × t (distance then = unit rate × other time)
Go along the line to the other time: rate × time.
d
=
12
×
2
d
=
24
mi
Check
Put the numbers back in. Both sides should match.
12 = 3 ÷ 0.25 ✓
24 = 12 × 2 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.