Equations Of Lines. Need Help. Thank you

Question

1)

The equation of a line is -x+2y=4. The equation of a line parallel to it is kx + 4y = 16. What is the value of k?

2)

The equation of a line is 3x - y = 6. The equation of a line perpendicular to it is 4x + ky = 12. What is the value of k?

3)

The equation of a line is Ax + By = C. What is the relations hip between A and B for any line parallel to the

4)

The equation of a line is Ax + By = C. What is the relationship between A and B for any line perpendicular to the initial line?

Answer 1

1)

The equation of a line is -x+2y=4. The equation of a line parallel to it is kx + 4y = 16. What is the value of k?

You may continue to convert to slope-intercept form (to get m), or you could notice that the slope of a line in Standard Form is (-A/B).

The slope of the line -x+2y=4 is 1/2.

All parallel lines have the same slope. So, k = -2

The parallel line is -2x+4y=16

2)

The equation of a line is 3x - y = 6. The equation of a line perpendicular to it is 4x + ky = 12. What is the value of k?

Perpendicular lines have slopes that are the negative reciprocals of each other. If the slope of this line is (3), then the slope of all perpendicular lines is (-1/3). So, k=12

The equation of the parallel line is 4x+12y=12

3)

The equation of a line is Ax + By = C. What is the relations hip between A and B for any line parallel to the

Since the slope is (-A/B) for this line, every parallel line will have the same slope (-A/B)

4)

The equation of a line is Ax + By = C. What is the relationship between A and B for any line perpendicular to the initial line?

Since the slope of this line is (-A/B) then the slope of all perpendicular lines is (B/A).

Comment: You should be very thankful that this problem uses the Standard Form (Ax+By=C) so you can learn to calculate slope without always converting to slope-intercept form. Many books, teachers, and tutors miss this completely (and it is a great time-saver on homework and standardized tests like the ACT or SAT).

Answer 2

#1: First, convert both equations to the standard form: y=mx + b. From the first equation, you know the value of m. Substitute that value of m in the second equation and solve for k.

#2: The process is the same as for #1, except recall that for perpendicular lines the slope of the perpendicular is the inverse reciprocal of the original slope. If you have a line with m=4, the perpendicular line has slope -1/4.

#3: Put the equation in the standard form. The slope is always the same for parallel lines. What does this tell you about the relationship between A and B?

#4: Put the equation in the standard form. The slope of the perpendicular line is the inverse reciprocal of the original slope. What does this tell you about the relationship between A and B?