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

step 1 Let's start by finding the slope of the given line. So let's isolate y. We have 4y equals negati

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. They have identical slopes, so when constructing a line parallel to a given line, you use the same slope as the original line regardless of the y-intercept.

Perpendicular Lines

Perpendicular lines intersect at a right angle (90°). Their slopes are negative reciprocals of one another (except in cases where one line is horizontal and the other is vertical, which have slopes of 0 and undefined, respectively), ensuring that the product of their slopes is -1 or that one line is vertical while the other is horizontal.

Slope-Intercept Form

The slope-intercept form of a line is written as y = mx + b, where m represents the slope and b represents the y-intercept. This form makes it easy to see the rate of change (slope) and the point where the line crosses the y-axis, which is essential for graphing and analysis.

Point-Slope Form

The point-slope form is a method of writing the equation of a line when you know a point on the line (x?, y?) and its slope m. It is given by y - y? = m(x - x?) and is particularly useful for deriving other forms of the equation, such as the slope-intercept form.

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