Write an equation of the line that contains the specified point and is perpendicular to the indi

step 1 To write the equation of the line that's perpendicular to 4x minus 2y equals 4, we first need to

Write an equation of the line that contains the specified...

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Key Concepts

Perpendicular Lines

Perpendicular lines are pairs of lines that intersect at a right angle (90 degrees). In analytic geometry, the slopes of two nonvertical perpendicular lines have a special relationship: the product of their slopes is -1. This means that if one line has a slope of m, then a line perpendicular to it will have a slope of -1/m.

Slope of a Line

The slope of a line measures its steepness and direction, calculated as the ratio of the change in y to the change in x between any two points on the line. Knowing the slope in different forms of a line equation is essential for understanding and relating different lines, especially when assessing perpendicularity.

Standard Form to Slope-Intercept Form Conversion

Many line equations are presented in standard form (Ax + By = C). Converting these equations to slope-intercept form (y = mx + b) is useful because it isolates the slope (m) and y-intercept (b), making it easier to analyze the line's behavior and relationships with other lines, such as determining perpendicular slopes.

Point-Slope Form

The point-slope form of a line equation, given by y - y1 = m(x - x1), is highly practical when you are provided with a point on the line and its slope. This form directly incorporates these elements, making it straightforward to derive the equation of a line under specific conditions.

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