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.
$(-3.9,-1.4), 6 x+2 y=9$

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Key Concepts

Point-Slope Form

The point-slope form of a line is expressed as y - y? = m(x - x?), where m is the slope and (x?, y?) is a point on the line. This form is particularly useful when a specific point and the slope of the line are known, serving as an intermediate step before converting to slope-intercept form.

Perpendicular Lines

Perpendicular lines intersect at a right angle (90 degrees), and their slopes are negative reciprocals of each other. This means if one line has a slope m, the slope of a perpendicular line will be -1/m, provided m is not zero.

Parallel Lines

Parallel lines in the same plane have the identical slope, meaning they rise and run at the same rate. Because of this commonality in slope, parallel lines never intersect.

Slope-Intercept Form

The slope-intercept form of a line is written as y = mx + b, where m represents the slope of the line (its steepness) and b indicates the point at which the line crosses the y-axis (the y-intercept). This form is useful for quickly identifying the key characteristics of the line.

Slope

The slope is a measure of how steep a line is and is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between any two distinct points on the line. It plays a crucial role in determining the direction of the line.

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