Linear models
Linear models is a Grade 7 math skill from Yoshiwara Intermediate Algebra where students use linear equations to represent real-world situations with a constant rate of change. Students write, interpret, and apply linear models to predict values and understand trends in data.
Key Concepts
Property Linear models have equations of the form: $$y = \text{(starting value)} + \text{(rate of change)} \cdot x$$.
Examples It costs 2000 dollars to develop a calculator and 20 dollars to manufacture each one. The total cost, $C$, for $n$ calculators is $C = 2000 + 20n$.
The world's oil reserves were 2100 billion barrels and decrease by 28 billion barrels per year. The remaining reserves, $R$, after $t$ years is $R = 2100 28t$.
Common Questions
What is a linear model?
A linear model represents a real-world situation with a linear equation y = mx + b, where m is the rate of change and b is the initial value.
How do you interpret the slope in a linear model?
The slope represents the rate of change — how much y changes for each unit increase in x. For example, a slope of 3 means the output increases by 3 for each unit increase in input.
How do you write a linear model from a word problem?
Identify the rate of change (slope) and starting value (y-intercept), then write y = mx + b.
How accurate are linear models for predicting future values?
Linear models are accurate within the observed data range. Predictions far outside the range (extrapolation) become less reliable if the true relationship is nonlinear.