What this lesson covers
- y = mx + b: b is the value at x = 0, m is the change per ONE unit of x
- The money beat: a plumber's C = 45h + 80, translated both ways
- The twist: S = 500 - 40d, where a negative rate is still a rate
- Practice: R = 15t + 40, which statement is true?
- The three traps that eat most wrong answers
Questions worked in the video
- 0:58A plumber charges C = 45h + 80, where h is hours worked. What do 45 and 80 represent?
- 1:40S = 500 - 40d gives the sheets left after d days. Interpret 500 and -40.
- 2:12R = 15t + 40, where R is total dollars and t is hours tutored. Which statement is true?
Chapters
- 0:00Intro
- 0:04An equation you do not solve
- 0:24The anatomy of y = mx + b
- 0:58The money beat: C = 45h + 80
- 1:40The twist: a negative rate
- 2:12Practice: R = 15t + 40
- 2:50Three traps
- 3:21Recap
Lesson transcript
The narration of the video, word for word, under its chapter headings.
0:04An equation you do not solve
Welcome to SAT Climb. Here is an equation the SAT does not want you to solve. Cost equals 45h plus 80. There is nothing to solve. The whole question is what the 45 means, and what the 80 means. That is a translation problem.
0:24The anatomy of y = mx + b
Every linear model looks the same. y equals mx plus b. The b is the starting value, what you have when x is zero, before anything happens. On the graph it is where the line crosses the vertical axis. The m is the rate. It tells you how much y changes for every one unit x goes up. On the graph it is the size of one step. Starting value, and rate per one. Those are the only two things a linear model can tell you, and the SAT asks about them over and over.
0:58The money beat: C = 45h + 80
Here is the classic question. A plumber charges cost equals 45h plus 80, where h is the number of hours worked. What does the 80 represent? Set h to zero. Zero hours of work, and the cost is already 80 dollars. So 80 is a flat fee, charged before any hours happen. Now the 45. Move one hour to the right, and the cost climbs by 45 dollars. Every single hour, another 45. So 45 is the price per hour. 80 to show up. 45 an hour after that.
1:40The twist: a negative rate
Now the twist the test loves. Sheets equals 500 minus 40d, where d is days. The 500 still works the same way. At day zero, there are 500 sheets in the tray. But the rate is negative. Every day, the stack drops by 40 sheets. Negative does not mean the rate is broken. It means the direction is down. 40 sheets used per day. So read the sign, then read the number, then attach the units.
2:12Practice: R = 15t + 40
Your turn. R equals 15t plus 40, where R is total dollars charged and t is hours tutored. Which statement is true? Pause and think. Here is the read. 40 sits alone, so it is the flat fee, 40 dollars before any tutoring. 15 is attached to t, so it is 15 dollars per hour. That is answer B. 15 dollars an hour plus a 40 dollar flat fee.
2:50Three traps
Three traps. One, swapping the two numbers. The number attached to the variable is the rate. The number sitting alone is the starting value. Two, dropping the per one. 45 is not 45 dollars total, it is 45 dollars for each hour. Three, ignoring the sign. A negative rate is still a rate. It just means the quantity is going down by that much each time. Slope is per one. Intercept is at zero.
3:21Recap
Linear models, solved. The number attached to x is the rate, per one unit. The number sitting by itself is the value when x is zero. Translate the two numbers, attach the units, and the question is already done. Start free at satclimb.com.
Read the written version: the Linear functions strategy guide, then try 25 hard Linear functions questions with full explanations. Both are free, no account needed.