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

In Exercises 67-76, write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.
$\left(\frac{2}{5},-1\right), \quad 3 x-2 y=6$

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Key Concepts

Slope-Intercept Form

The slope-intercept form, written as y = mx + b, is a way of expressing the equation of a line where m represents the slope and b represents the y-intercept. This form makes it easy to see both the steepness of the line and the point at which it crosses the y-axis.

Point-Slope Form

The point-slope form of a line, given by y - y? = m(x - x?), is used to create an equation of a line when a specific point on the line (x?, y?) and its slope m are known. It serves as an intermediate step before rearranging the equation into a different form like slope-intercept form.

Parallel Lines

Parallel lines are characterized by having the same slope. When constructing the equation of a line that is parallel to a given line, the slope of the new line is identical to that of the original line, ensuring they never intersect.

Perpendicular Lines

Perpendicular lines intersect at right angles. An important property of perpendicular lines is that their slopes 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.

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