Math 1 · Unit 3 · Lesson 5 · part 2 of 6
Read m and b in a story
y = mx + b in a story is easy to read once you know the two jobs.
Read m and b in a story
y = mx + b in a story is easy to read once you know the two jobs. b is the starting amount: what you have at the beginning, the flat fee, the amount when x is 0. m is the rate: the per hour, per month, per mile, per ticket, how much y changes for each one of x. Read both, and you can write the equation straight from the description.
A taxi
$3 to get in, then $2 per mile. Start: 3. Rate: 2 per mile.
cost = 2m + 3, where m is miles.
A 10-mile ride: 2 × 10 + 3 = 23 dollars.
A savings jar
Starts with $40, add $15 every week. Start: 40. Rate: 15 per week.
money = 15w + 40.
After 6 weeks: 15 × 6 + 40 = 130 dollars. When is it 250? 250 = 15w + 40, so 15w = 210, so w = 14 weeks.
A draining tank (negative rate)
Holds 500 gallons, loses 20 gallons a minute. Start: 500. Rate: −20 per minute, because it is going down.
gallons = −20t + 500.
Empty when y = 0: 0 = −20t + 500, so t = 25 minutes. That is the x-intercept from Lesson 4: when the story hits zero.