Linear model
Linear model is a Grade 7 math topic from Yoshiwara Intermediate Algebra where students use linear equations to model real-world data. A linear model predicts values based on a constant rate of change and is represented by a line of best fit or an exact equation from two data points.
Key Concepts
Property A linear model describes a variable that increases or decreases at a constant rate. It has the form.
$$y = \text{(starting value)} + \text{(rate)} \times t$$.
Examples April's income is 200 dollars per week plus 9% commission on sales $S$. Her income $I$ is $I = 200 + 0.09S$.
Common Questions
What is a linear model in mathematics?
A linear model uses a linear equation y = mx + b to describe and predict the relationship between two quantities that change at a constant rate.
How do you create a linear model from data?
Plot the data, identify a linear trend, choose two representative points, calculate the slope, and write the equation using point-slope form.
When is a linear model appropriate?
A linear model is appropriate when the data shows a constant rate of change — the scatter plot looks like a straight-line pattern.
How do you use a linear model to make predictions?
Substitute the input value into the linear equation and calculate the output. Predictions within the data range (interpolation) are more reliable than extrapolation.