Download 1. write an equation of the line containing the given

1. write an equation of the line containing the given point and PARALLEL to the given
line. Express your answer in the form y= mx+b. (4, 9); x + 7y = 6 The equation of the
line is y= ???
Step 1: Rewrite the given equation in y = mx+b form.
x + 7y = 6
7y = -x +6
y = -(1/7)x + 6/7
Step 2: Determine the slope of the given line.
When the equation is in y = mx + b form, the slope of the line is m.
The slope of the given line is -1/7
Step 3: Determine the slope of the new line.
Since the new line is parallel to the given line, they will have the same
slope. Therefore, for the new line, m = -1/7
Step 4: Write equation for new line, with unknown b.
y = (-1/7)x + b
Step 5: Substitute the given point and solve for b.
9 = (-1/7)(4) + b
9 = -4/7 + b
b = 9 + 4/7
b = 63/7 + 4/7
b = 67/7
Step 6: Write the equation of the new line:
y = (-1/7)x + 67/7
2. write an equation of the line containing the given point and PARALLEL to the given
line. Express your answer in the form y= mx+b. (-2, 9); 6x = 5y + 2 The equation of the
line is y= ???
Same steps as the previous problem:
Step 1:
6x = 5y + 2
5y = 6x – 2
y = (6/5)x – 2/5
Step 2:
slope = 6/5
Step 3:
Lines are parallel, so the slope of the new line is also 6/5
Step 4:
New line: y = (6/5)x + b
Step 5:
9 = (6/5)(-2) + b
9 = -12/5 + b
b = 45/5 + 12/5
b = 57/5
Step 6:
y = (6/5)x + 57/5
3. write an equation of the line containing the given point and PERPENDICULAR to the
given line. (3, 9); 8x + y = 6 The equation of the line is y= ???
This is the same as the previous two problems, except for a small twist involving
the slope of the new line.
Step 1:
8x + y = 6
y = -8x + 6
Step 2:
slope of given line: m = -8
Step 3:
Since the new line is perpendicular to the given line, its slope will be
the negative reciprocal of the given line’s slope.
new slope = -1/m = -1/-8 = 1/8
Step 4:
y = (1/8)x + b
Step 5:
9 = (1/8)3 + b
9 = 3/8 + b
b = 9 – 3/8
b = 72/8 – 3/8
b = 69/8
Step 6:
y = (1/8)x + 69/8
4. write an equation of the line containing the given point and PERPENDICULAR to the
given line. (6, -7); 9x + 2y = 7
Same procedure as #3
Step 1:
9x + 2y = 7
2y = -9x + 7
y = (-9/2)x + 7/2
Step 2:
m = -9/2
Step 3:
slope of new line = -1/m = -1/(-9/2) = 2/9
Step 4:
y = (2/9)x + b
Step 5:
-7 = (2/9)(6) + b
-7 = 12/9 + b
b = -7 – 12/9
b = -63/9 – 12/9
b = -75/9
Step 6:
y = (2/9)x – 75/9