In Exercises 13-16, write an equation of the line passing...

In Exercises $13-16,$ write an equation of the line passing through point $\mathrm{P}$ that is parallel to the given line. Graph the equations of the lines to check that they are parallel. (See Example $3 . )$

$$P(-2,6), x=-5$$

Key Concepts

Point-Slope Form

The point-slope form of a line is a useful formulation for writing a linear equation when one point on the line and the slope are known. It is expressed as y - y? = m(x - x?), where (x?, y?) is a specific point and m is the slope. This form is particularly effective when finding the equation of a line parallel to a given line by using the same slope.

Parallel Lines

Parallel lines are lines that never intersect because they have identical slopes. In coordinate geometry, if one line has a given slope, any line parallel to it must have the same slope. This concept is essential when writing equations of lines that maintain a fixed orientation relative to one another.

Vertical Lines

Vertical lines are characterized by having all points sharing the same x-coordinate, and they are represented by equations in the form x = constant. Due to their vertical orientation, they have an undefined slope, and any vertical line is parallel to another vertical line, which is significant when identifying parallelism in problems involving vertical lines.

Equation of a Line

The equation of a line in the coordinate plane is a mathematical expression that describes all the points lying on that line. Different forms of linear equations include slope-intercept form, point-slope form, and standard form. Choosing the appropriate form depends on the information available, such as a point on the line and its slope.

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