This simple interest model A = 1000 + 50t shows account balance A where t is years. The y-intercept 1000 is the initial principal, and slope 50 is the annual interest earned. After 5 years, total balance is A = 1000 + 50(5) = 1250. The interest earned is the difference: 1250 - 1000 = $$\250$$. Choice A confuses total balance with interest earned.

This is a linear growth model where h represents height and d represents days. The slope of 2 means the plant grows 2 cm per day. The y-intercept of 5 represents the initial height when d = 0 days. The equation h = 5 + 2d correctly models this relationship where current height equals initial height plus growth over time. Choice D incorrectly reverses the coefficients, making the initial height 2 cm and growth rate 5 cm per day.

In the phone plan equation y = 0.10x + 25, we need to identify what each variable represents based on the context. The equation models total monthly cost where y represents the total cost, 25 represents the fixed monthly fee, and 0.10 represents the cost per text message. Therefore, x must represent the number of text messages sent, since it's the variable being multiplied by the per-text rate. The structure follows the pattern: total cost = (rate per text)(number of texts) + fixed fee.

This is a distance calculation using constant speed where distance = speed × time. The train travels at 80 kilometers per hour for 3.5 hours. Using the relationship: distance = speed × time, we get 80 km/hour × 3.5 hours = 280 kilometers. This represents the total distance covered when traveling at constant speed for the given time duration. The calculation involves multiplying the rate by the time period.

This is a linear altitude model where y represents altitude and x represents time in minutes. The slope of -5 means the altitude decreases by 5 meters per minute (negative because it's descending). The y-intercept of 200 represents the initial altitude when x = 0 minutes. The equation y = 200 - 5x correctly models this decreasing relationship. Choice B incorrectly uses a positive slope, which would represent ascending rather than descending. Choice A uses the wrong rate of change.

This cost model $C = 500 + 3x$ represents manufacturing costs where $C$ is total cost and $x$ is units produced. The y-intercept $500$ represents the fixed cost - costs that remain constant regardless of production level (like rent, equipment, insurance). The slope $3$ represents variable cost per unit. Choice B confuses the variable cost with fixed cost.

This is a linear growth model where y is plant height in inches and x is weeks since purchase. The plant starts at 6 inches (when x = 0), making 6 the y-intercept. The plant grows 1.5 inches per week, making 1.5 the slope. The equation is y = 1.5x + 6. Choice A incorrectly reverses the slope and intercept, putting 6 as the growth rate and 1.5 as the starting height. Choices C and D use negative slopes, which would mean the plant is shrinking.

This models a candle burning at constant rate where y is height in cm and x is time in hours. At x = 0, the candle is 18 cm tall (y-intercept = 18). At x = 3, it's 12 cm tall. The candle lost 6 cm in 3 hours, so the rate is -2 cm per hour (slope = -2). The equation is y = -2x + 18. Choice A uses positive slope, meaning the candle would grow taller. Choice C has slope -6, which would mean the candle loses 6 cm per hour instead of per 3 hours.

The model y = 0.25x represents distance (y in meters) versus time (x in seconds) for a runner. The slope 0.25 means the runner's distance increases by 0.25 meters for each second that passes - this is the runner's speed of 0.25 meters per second. There is no y-intercept term, meaning the runner starts at the starting line (0 meters when x = 0). Choice C incorrectly inverts the units to seconds per meter. Choice A misinterprets the slope as a starting position.

In the linear model y = 30x + 80 for gym costs, y is total cost and x is months. The slope (coefficient of x) is 30, which represents the rate of change - the cost increases by $30 for each additional month. This is the monthly fee. The y-intercept 80 is the initial cost when x = 0, representing the one-time sign-up fee. Choice B incorrectly identifies the slope as the sign-up fee instead of recognizing it as the monthly rate.