Page 27 - Algebra

Worked Example
Find the equation of line passing through (2, 1) and is parallel and perpendicular to 3x – y = 4
Solution:
Write the equation in the form of y = mx + c Slope of two parallel lines is always the same
3x – y = 4
y = 3x – 4
m=3
Now use the point-slope form equation. The equation passes through (2, 1) y–y1 =m(x–x1)
y – 1 = 3(x – 2)
y – 1 = 3x – 6
y = 3x – 5
The line parallel to 3x – y = 4 is y = 3x – 5
Product of two parallel lines is –1
Slope of the first line = 3
Slope of the perpendicular line = m1m2 = –1
3m2 = –1
1
m2 = –
3
Use the slope in the point-slope form y–y1 =m(x–x1)
y–1=– (x–2)
3
3y – 3 = –x + 2 3y = –x + 5
The line parallel to 3x – y = 4 is 3y = –x + 5
1
Page 26 of 177
Algebra I & II