Write a linear function from data (points/table) and use it to make predictions. | Linear functions | SAT Math

Build a linear model from data, then use the equation to predict new values.

核心知识

To model data with a linear function, find the slope from two data points, solve for the y-intercept, then substitute any input value to predict the corresponding output.

深入理解

Build the line first, then predict. SAT questions often give you data and ask for a value that is not in the table.

Find the slope from two data points.
Use one point in $𝑦 = 𝑚 𝑥 + 𝑏$ to solve for $𝑏$ .
Plug in the target input value to make the prediction.

If the question asks beyond the given data range, the same line still works mathematically. Just be ready to judge whether the prediction is reasonable in context.

分步讲解

Identify two data points from the problem (table rows, described values, or graph points).
Calculate the slope: $𝑚 = 𝑦 2 - 𝑦 1 𝑥 2 - 𝑥 1$ .
Solve for the y-intercept by substituting one point into $𝑦 = 𝑚 𝑥 + 𝑏$ .
Write the complete equation, then substitute the target input value to find the prediction.

常见误解

Using only one data point and guessing the slope — you always need at least two points to determine a unique line.
Forgetting to solve for $𝑏$ and assuming it's zero — unless the data passes through the origin, $𝑏 \neq 0$ .
Rounding the slope mid-calculation and getting a slightly wrong prediction — keep exact values until the final answer.

题目

示例解析

A biologist records that a plant is 4 cm tall after 3 days and 10 cm tall after 6 days. Assuming the plant grows at a constant rate, what is the predicted height, in cm, after 10 days?

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