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.
$(-1.2,2.4), 5 x+4 y=1$

Key Concepts

Slope-Intercept Form

The slope-intercept form of a line is written as y = mx + b, where m represents the slope of the line, and b represents the y-intercept, which is the point where the line crosses the y-axis. This form is useful because it directly shows the rate of change (slope) and the starting value (y-intercept) of the line.

Parallel Lines

Parallel lines in a plane have the same slope. This means that if you have a given line with a known slope, any line parallel to it will share that identical slope. This property is crucial when finding the equation of a line parallel to another, as only the y-intercept might differ while the slope remains consistent.

Perpendicular Lines

Perpendicular lines are lines that intersect at a right angle (90 degrees). In terms of slopes, if one line has a slope m, then a line perpendicular to it will have a slope that is the negative reciprocal, which is -1/m, provided that m is not zero. This relationship is essential in identifying and constructing lines that are orthogonal to a given line.

Converting from Standard Form

When a line is presented in standard form, typically in the format Ax + By = C, it is necessary to convert it to the slope-intercept form to easily identify its slope. By solving the equation for y, the slope can be derived as -A/B. This conversion is crucial for tasks involving finding parallel or perpendicular lines since knowing the slope of the original line is required.

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