Linear Functions and Linear Regression

Vocabulary flashcards covering linear modeling tools, linear regression procedures on graphing calculators, and interpreting linear components in context.

Slope-Intercept Form

The linear equation tool $y = mx + b$, where $m$ represents the slope (rate of change) and $b$ represents the y-intercept.

Point-Slope Form

The linear equation tool $y - y_1 = m(x - x_1)$, used to model a line when given a rate of change and a point that is not the y-intercept.

Slope Formula

The formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, used to calculate the rate of change given two points by finding the change in $y$ over the change in $x$.

Slope

The rate of change in a linear function, defined as the rise over run or the amount the $y$-variable changes for every unit change in $x$.

y-intercept

The initial value or starting point of a line, representing the value of $y$ when $x = 0$ where the graph crosses the y-axis.

DiagnosticOn

A setting on the graphing calculator accessed via second then 0 that must be enabled to view the correlation coefficient ($r$) during linear regression.

Linear Regression (LinReg)

A technology feature under stat -> calc (Option 4) that calculates the best-fit line equation $y = ax + b$ for a data set.

Correlation Coefficient ($r$)

A value produced during regression analysis that measures the strength and direction of a linear relationship, where values closer to $1$ or $-1$ indicate higher accuracy.

Strong Positive Correlation

A linear relationship where the correlation coefficient ($r$) is close to $1$ and the slope is positive, meaning $y$ increases as $x$ increases.

Strong Negative Correlation

A linear relationship where the correlation coefficient ($r$) is close to $-1$ and the slope is negative, meaning $y$ decreases as $x$ increases.