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Understanding the slope-intercept form of a line is essential when dealing with linear equations. The slope-intercept form is written as: \[y = mx + c\] where \(m\) is the slope of the line, and \(c\) is the y-intercept. This form is useful as it directly shows the slope \(m\) and the point where the line crosses the y-axis, \(c\). A few points to keep in mind:

• The slope \(m\) describes the steepness or incline of the line. A positive slope means the line is ascending, while a negative slope indicates the line is descending.
• For example, if \(m = -1\), as in the exercise, the line falls down one unit vertically for each unit it moves horizontally.
• The y-intercept \(c\) represents the line's starting point on the y-axis when \(x = 0\).

These concepts are important for visualizing and understanding how a line behaves on a graph. By being familiar with the slope-intercept form, you can easily write and interpret the equation of any straight line.

Degrees and radians are two units of measuring angles, and sometimes it’s necessary to convert between them. The conversion formula you can use is: \[Degrees = Radians \times \frac{180}{\pi}\] This formula comes from the relationship that \(180\) degrees is equivalent to \(\pi\) radians. Converting an angle from radians to degrees involves multiplying by the constant \(\frac{180}{\pi}\).In the exercise, the inclination of the line is first calculated in radians as \(-\frac{\pi}{4}\). To convert this to degrees:

• Step 1: Multiply \(-\frac{\pi}{4}\) by \(\frac{180}{\pi}\).
• Step 2: This results in \(-45\) degrees.

Simple and straightforward, this conversion allows you to express angles in a format that might be more intuitive, especially if you are more accustomed to thinking of angles in terms of degrees.

The arctangent function, often denoted as \(\arctan\), is the inverse function of the tangent. Given a slope \(m\), the arctangent function helps us find the angle \(\theta\) whose tangent is \(m\). The basic property is:- If \(\theta = \arctan(m)\), then \(\tan(\theta) = m\).As seen in the exercise, the function \(\arctan(-1)\) gives the angle whose tangent is \(-1\). The result is \(-\frac{\pi}{4}\) radians.Key points about \(\arctan\):

• The range of \(\arctan(x)\) is \(-\frac{\pi}{2}\) to \(\frac{\pi}{2}\) radians, which means it yields values only in this interval.
• Using \(\arctan\) is a common way to find the inclination of a line when only the slope is known.
• This function is particularly useful for converting a slope into a specific directional angle.

By understanding how the arctangent function operates, you can determine the precise angle of inclination for any line with a known slope.