1. Let's start by understanding the concept of a line equation. A line in a plane can be represented by the equation: $$y = m x + c$$ where: - $y$ is the value at any point on the line corresponding to $x$. - $m$ is the slope of the line. - $c$ is the y-intercept, which is the value of $y$ when $x=0$. 2. The slope $m$ of a line measures how steep the line is. It is calculated as the rise over run, meaning: $$m = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}$$ This tells us how much $y$ increases or decreases as $x$ increases by 1. 3. The intercept $c$ is the point where the line crosses the y-axis. When $x=0$, the line's value is $y=c$. 4. Now, about mean and variance: - Mean is the average of a set of numbers. If you have values $x_1, x_2, \ldots, x_n$, the mean $\bar{x}$ is: $$\bar{x} = \frac{1}{n} \sum_{i=1}^n x_i$$ - Variance measures how spread out the numbers are around the mean. It is: $$\text{Variance} = \frac{1}{n} \sum_{i=1}^n (x_i - \bar{x})^2$$ These concepts form the foundation for understanding lines and data distribution, which are crucial in algebra and statistics.