Question

Answer any of the following questions:
1. Write the equation of the line which passes through (5, –2) and is parallel to x = 4.
2. Write the equation of the line which passes through (2, 1) and is perpendicular to x = –2.
3. Write the equation of the line which passes through (–4, 2) and is parallel to y = –x + 6 in slope-intercept form.
4. Write the equation of the line which passes through (2, –3) and is perpendicular to y = 4x + 7 in standard form.
5. Using complete sentences, describe one example of a place in your everyday life of parallel lines and one example of perpendicular lines

Answer 1

1.) parallel lines has equal slopes. Line x = 4 is a vertical line, hence required line is a verticsl line with equation x = 5.

2.) the line x = -2 is a vertical line, hence required line is a horizontal line with equation y = 1.

3.) line y = -x + 6 has a slope of -1, hence, required equation is y - y1 = -1(x - x1)
y - 2 = -(x - (-4))
y - 2 = -(x + 4)
y - 2 = -x - 4
y = -x - 4 + 2
y = -x - 2

Answer 2

The equation of the line has a general formula of y = mx+b

1. Write the equation of the line which passes through (5, –2) and is parallel to x = 4. 
The equation of the line that is parallel to x =4 would be an equation that the never intersect y and has an infinite slope. So, the equation should be x = 5.

2. Write the equation of the line which passes through (2, 1) and is perpendicular to x = –2. 
The equation should be x = 2.

3. Write the equation of the line which passes through (–4, 2) and is parallel to y = –x + 6 in slope-intercept form.
The slope of the line should be equal to the given equation. 
y - 2 = -1(x - (-4))
y = -x + 6


4. Write the equation of the line which passes through (2, –3) and is perpendicular to y = 4x + 7 in standard form. 
The slope of the line should be the negative reciprocal to the given equation. 
y - -3 = -1/4(x - (2))
y = -1/4 x - 5

5. Using complete sentences, describe one example of a place in your everyday life of parallel lines and one example of perpendicular lines.
Parallel lines - sides of a book
Perpendicular lines - window pane