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Answer:
1) 2x+7
2) -3x+11
3) 0.75x-2
4) -2x+0
5) -1.5x+2
6) -4x+16
Step-by-step explanation:
1) y = mx + c
m = 2 when x=1 , y=9
9 = 2(1)+c
c = 7
y = 2x + 7
2) m = -3
When x=4, y= -1
-1 = -3(4) + c
c = -1+12 = 11
y = -3x + 11
3) m = 0.75
When x= -4, y= -5
-5 = 0.75(-4) + c
-5 = -3 + c
c = -2
y = 0.75x - 2
4) m = (y2-y1)/(x2-x1)
m = (2-(-6))/(-1-3) = 8/-4 = -2
y = -2x + c
When x= -1, y= 2
2 = -2(-1) + c
2 = 2 + c
c = 0
y = -2x + 0
5) m = (-10-(-4))/(8-4)
m = (-10+4)/4 = -6/4 = -1.5
y = -1.5x + c
When x= 4, y= -4
-4 = -1.5(4) + c
-4 = -6 + c
c = 2
y = -1.5x + 2
6) m = (-4-4)/(5-3) = -8/2 = -4
When x= 3, y= 4
4 = -4(3) + c
4 = -12 + c
c = 16
y = -4x + 16
Amalia. Phones rule is only true with numbers between 1 and 1,000.
4, 5, and 7 are mutually coprime, so you can use the Chinese remainder theorem right away.
We construct a number
such that taking it mod 4, 5, and 7 leaves the desired remainders:

- Taken mod 4, the last two terms vanish and we have

so we multiply the first term by 3.
- Taken mod 5, the first and last terms vanish and we have

so we multiply the second term by 2.
- Taken mod 7, the first two terms vanish and we have

so we multiply the last term by 7.
Now,

By the CRT, the system of congruences has a general solution

or all integers
,
, the least (and positive) of which is 27.
Because 3*6= 18 and 18/2 equals 9. So therefore they are NOT equal.