In Exercises 67-76, write the slope-intercept forms of the equations of the lines through the gi

step 1 We're going to start by finding the slope of the given line, and so we can isolate y, and we get

In Exercises 67-76, write the slope-intercept forms of the...

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Key Concepts

Parallel Lines

Parallel lines are lines in the same plane that never intersect, and they have identical slopes. This property allows us to write the equation of a line parallel to a given line by using the same slope as the given line and adjusting the intercept to ensure it passes through a specific point.

Perpendicular Lines

Perpendicular lines intersect at a right angle (90 degrees). Their slopes are negative reciprocals of each other, meaning if one line has a slope m, the perpendicular line will have a slope of -1/m. This relationship is central for determining the equation of a line that is perpendicular to a given line.

Slope-Intercept Form

The slope-intercept form is a way to express the equation of a line in the format y = mx + b, where m represents the slope of the line and b represents the y-intercept. It is useful for quickly identifying the slope and intercept, and for graphing linear equations.

Point-Slope Form

The point-slope form is used to write the equation of a line when you know its slope and a single point on the line. It is written as y - y? = m(x - x?), where (x?, y?) is the point and m is the slope. This form is particularly useful when deriving the slope-intercept form by algebraic manipulation.

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