4.3 Writing Equations of Parallel/Perpendicular

Writing equations of parallel and perpendicular shall be easy.

Remember this:

Parallel line means: these two lines have the same slope. (m1=m2)

Perpendicular line means: these two lines' slope are negative reciprocal relationship.(m1 * m2 = -1)

To write the equation of a line that is parallel to another line, follow these steps:

1. Find the slope (m) of the given line.

2. Use the slope of the given line to find the slope of the parallel line. Remember, parallel lines have the same slope.

3. Use the point-slope form of a linear equation to write the equation of the parallel line. This form is y - y1 = m(x - x1), where (x1, y1) is any point on the line.

4. Simplify the equation if necessary by rearranging the terms to slope-intercept form (y = mx + b).

For example, suppose you are given the equation of a line as y = 2x + 1, and you need to write the equation of a line that is parallel to this line and passes through the point (3, 5). To write the equation of the parallel line, follow these steps:

1. The slope of the given line is m = 2.

2. Since the parallel line has the same slope, the slope of the parallel line is also m = 2.

3. Use the point-slope form of the linear equation to write the equation of the parallel line:

y - y1 = m(x - x1)

y - 5 = 2(x - 3)

1. Simplify the equation by rearranging the terms to slope-intercept form:

y = 2x - 1

So the equation of the line that is parallel to y = 2x + 1 and passes through the point (3, 5) is y = 2x - 1.

Writing equations of parallel and perpendicular shall be easy.

Remember this:

Parallel line means: these two lines have the same slope. (m1=m2)

Perpendicular line means: these two lines' slope are negative reciprocal relationship.(m1 * m2 = -1)

To write the equation of a line that is perpendicular to another line and passes through a given point, follow these steps:

1. Find the slope (m) of the given line.

2. Find the slope of the line that is perpendicular to the given line. Remember, perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of the given line is m, then the slope of the perpendicular line is -1/m.

3. Use the point-slope form of a linear equation to write the equation of the perpendicular line. This form is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the perpendicular line.

4. Simplify the equation if necessary by rearranging the terms to slope-intercept form (y = mx + b).

For example, suppose you are given a line with the equation y = 2x + 1 and you need to write the equation of a line that is perpendicular to this line and passes through the point (3, 5). To write the equation of the perpendicular line, follow these steps:

1. The slope of the given line is m = 2.

2. Since the perpendicular line has a slope that is the negative reciprocal of 2, the slope of the perpendicular line is -1/2.

3. Use the point-slope form of the linear equation to write the equation of the perpendicular line:

y - y1 = m(x - x1)

y - 5 = (-1/2)(x - 3)

1. Simplify the equation by rearranging the terms to slope-intercept form:

y = (-1/2)x + 7/2

So the equation of the line that is perpendicular to y = 2x + 1 and passes through the point (3, 5) is y = (-1/2)x + 7/2.

Writing equations of parallel and perpendicular shall be easy.

Remember this:

Parallel line means: these two lines have the same slope. (m1=m2)

Perpendicular line means: these two lines' slope are negative reciprocal relationship.(m1 * m2 = -1)