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The slope of a line is a measure of its steepness and direction. In mathematics, slope is usually denoted by the letter \( m \). Slope is calculated as the rise over the run, which means it is the change in the y-coordinate divided by the change in the x-coordinate between two distinct points on the line.

For example, if you have two points, \( (x_1, y_1) \) and \( (x_2, y_2) \), the slope \( m \) can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] In our exercise, the slope is given directly as 1. This means for each unit increase in x, y increases by 1 unit.

The y-intercept of a line is the point where the line crosses the y-axis of a graph. This is the value of y when x is zero. In the slope-intercept form of a linear equation \( y = mx + b \), the y-intercept is represented by the letter \( b \).

In our exercise, the y-intercept is given as -1, which means the line crosses the y-axis at (0, -1). This tells us that when x is zero, y will be -1.

Understanding where the line crosses the y-axis provides a starting point for graphing the line and understanding its behavior.

A linear equation describes a straight line on a graph. The most common form of a linear equation is the slope-intercept form, \( y = mx + b \). Here, \( y \) is the dependent variable, \( x \) is the independent variable, \( m \) is the slope, and \( b \) is the y-intercept. This form makes it easy to quickly identify both the slope and y-intercept of the line.

For example, in the equation from our exercise, \( y = 1x - 1 \), it is clear that the slope \( m \) is 1 and the y-intercept \( b \) is -1. This allows us to draw the line by starting at the point (0, -1) on the y-axis and then using the slope to find other points on the line.

Linear equations are foundational in algebra and are used to model relationships where there is a constant rate of change.