standard form?

Question

1)is parallel to y=2x+6 and goes through (3,5)
2)is parallel to 3x+2y=8 and goes through (0,6)
3)is perpendicular to y=1/3x-8 and goes through (2,6)

Answer 1

1)is parallel to y=2x+6 and goes through (3,5)
y=2x+b
5=6+b
b=-1
y=2x-1
-2x+y=-1
2x-y=1

2)is parallel to 3x+2y=8 and goes through (0,6)
y=-3x/2+b
6=b
y=-3x/2+6
3x+2y=12

3)is perpendicular to y=1/3x-8 and goes through (2,6)
y=-3x+b
6=6+b
b=0
y=-3x
3x+y=0

Answer 2

Standard form for a linear equation is ax + by = c, and slope is -a/b. Parallel lines have the same slope, perpendicular lines have negative reciprocal slope. So...

1) slope is 2, so 2x - y = c must satisfy 2(3) - 5 = c, and so c = 1. thus 2x - y = 1

2) 3(0) + 2(6) = 12, so 3x + 2y = 12

3) perpendicular slope is -3, so 3x + y = c, and 3(2) + 6 = 12. thus 3x + y = 12

Answer 3

Well if the line is parallell it has the same gradient as the line ie. the number before the x.
Do a table for the y values and the x values where x is 2*y value (due to y=2x). It should work out that when y=5 x=10, therefore to get x to equal 3 you have to -7! Therefore it is y=2x-7...i think

For the second one, rearrange the equation to get y=....(divide by 2 to get y on its own) then its the same gradient....... as the one above method wise.

Thirdly, if its perpendicular...the rule is m1 x m2= -1 (so gradient 1 multiplied by gradient 2 = -1)
You know gradient one, therefore you can work out gradient 2 (grad 1 = 1/3 therefore grad2 = -3)
Then write out y=-3x+c (the new gradient in place of y=mx+c)
Then use the coordinates you've been given as in x=2, y=6 and sub that into the formula to find the value of c. Also this substitution method can be used in the first 2 questions.

Hope this helps

Answer 4

parallel means same slope
(y-5) = 2(x-3)
or y = 2x - 1

for 2) slope = -3/2
(y-6) = -3/2(x-0)
or y = -3/2x + 6

perpendicular slope is negative reciprocal
or -3
(y-6) = -3(x-2)
or y = -3x+12


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