Before you read

Answer first — see what you already know.

The equation $C = 0.08 m + 40$ gives the monthly cost $C$ (in dollars) of a water bill, where $m$ is water usage in gallons. What does $40$ represent?

A
The cost per gallon of water
B
The number of gallons used
C
The base monthly charge before water usage
D
The total bill for the month

Check your answer

Answer:

Before you read

Answer first — see what you already know.

A car's value is modeled by $V = 28, 000 - 3, 500 t$ , where $V$ is value in dollars and $t$ is years since purchase. What is the best interpretation of $- 3, 500$ ?

A
The car was purchased for $$3, 500$
B
The car's value decreases by $$3, 500$ each year
C
The car will be worthless in $3, 500$ years
D
The car loses $$3, 500$ in total

Check your answer

Answer:

Theory

The Big Three: Slope, Y-Intercept, and X-Intercept in Context

When a linear equation models a real situation ( $y = mx + b$ ):

Math	Real-world meaning
Slope ( $m$ )	The rate of change — how much $y$ changes for each 1-unit increase in $x$
Y-intercept ( $b$ )	The starting value — the value of $y$ when $x = 0$
X-intercept	The break-even or end point — the value of $x$ when $y = 0$

Monthly savings: $15/month starting at $200

The SAT tests your ability to connect these math concepts to their meaning in the problem's story.

Example 1

$P = 12t - 480$ models a company's monthly profit $P$ (dollars) based on $t$ shirts sold.

Interpret the slope, y-intercept, and find the x-intercept.

Slope = 12: Each additional shirt sold increases profit by $\$12$ (the profit per shirt).

Y-intercept = -480: When 0 shirts are sold, the company loses $\$480$ (fixed costs).

X-intercept: $0 = 12t - 480$ $\to$ $t = 40$ . The company needs to sell $40$ shirts to break even.

Slope =

12/shirt, y-intercept = -

480 (fixed costs), break-even at 40 shirts

Theory

Choosing the Right Model

Sometimes the SAT gives you a scenario and asks which equation best models it. Look for:

1. Is there a starting value? $\to$ That's $b$
2. Is there a rate per unit? $\to$ That's $m$
3. Is the quantity increasing or decreasing? $\to$ Positive or negative $m$

Common model types:
- Cost models: $C = \text{(cost per unit)} \cdot x + \text{(fixed cost)}$
- Distance/motion: $d = rt + d_0$
- Depreciation: $V = V_0 - rt$ (value decreases)
- Population/growth: $P = P_0 + rt$ (linear growth)

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2 more sections including examples, practice problems, and step-by-step solutions.

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