Write an equation in standard form of the line that contains the point (3,-5) and is a. parallel

step 1 In this problem, we're going to write the equation of the line that goes through the point 3 -5

Write an equation in standard form of the line that contains...

Key Concepts

Point-Slope Form

The point-slope form of a line's equation is an efficient way to write a line when you know its slope and a specific point it passes through. It is written as y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point. This form can later be manipulated into standard form if needed, making it a versatile tool in analytic geometry.

Perpendicular Lines

Perpendicular lines intersect at a right angle (90 degrees). The slopes of two perpendicular lines have a special relationship: they are negative reciprocals of each other. This means if one line has a slope m, the line perpendicular to it will have a slope of -1/m. This property is key when constructing the equation of a line that is required to be perpendicular to a given line.

Parallel Lines

Parallel lines are lines in the same plane that never intersect, which means they have identical slopes when expressed in slope-intercept form. To find the equation of a line parallel to a given line, you use the same slope as the original line and then adjust the equation so that it passes through the given point.

Standard Form Equation

Writing an equation in standard form involves rearranging it into the structure Ax + By = C, where A, B, and C are integers, and typically A is non-negative. This form is particularly useful for easily comparing different linear equations and identifying their coefficients directly.

Slope

The slope of a line represents its steepness and serves as a measure of the rate at which the line rises or falls as you move along it. It is calculated as the change in y divided by the change in x between any two points on the line. In problems involving parallel or perpendicular lines, determining or using the slope is essential because these types of lines have specific slope relationships.

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