Write an equation of the line parallel to the given line and...

Write an equation of the line parallel to the given line and containing the given point. Write the answer in slope-intercept form or in standard form, as indicated.
$x+2 y=22 ;(-4,7) ;$ standard form

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Key Concepts

Standard Form of a Linear Equation

The standard form of a linear equation is expressed as Ax + By = C, where A, B, and C are constants. This format is fundamental when working with linear equations because it clearly distinguishes the coefficients and is useful in various algebraic procedures, such as finding intercepts or comparing line equations.

Parallel Lines

Parallel lines are defined as lines that never intersect because they have the same slope. This property is critical when creating new line equations that are required to be parallel to a given line, ensuring that the new line shares the same directional incline as the original.

Slope Calculation from Standard Form

Given an equation in standard form, determining the slope is achieved by solving for y in terms of x to convert the equation to slope-intercept form (y = mx + b), where m represents the slope. This calculation is essential for identifying the direction of the line and for ensuring parallelism between lines.

Point-Slope Form

The point-slope form of a line’s equation is written as y - y? = m(x - x?), where (x?, y?) is a specific point on the line and m is the slope. This form is particularly useful when you know one point on the line and the slope, allowing you to construct the line’s equation directly.

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