You can use point-intercept formula, m=3/5, y1=-4, x1=2
(y-y1)=m(x-x1)
y+4=3/5(x-2)
y+4=(3/5)x-6/5
y=(3/5)x-6/5-4
y=(3/5)x-6/5-20/5
y=(3/5)x-26/5 or y=0.6x - 5.2
Answer to the slope and y-intercepts at the top:
#2: slope = -3 & y-intercept = (0,5)
#3: slope = 1 & y-intercept = (0, 4)
#4: slope = 5/6 & y-intercept = (0, -3)
#5: slope = -3 & y-intercept = (0, -7)
#6: slope = 1/5 & y-intercept = (0, 2)
Answers for the equations at bottom:
#5: y = 4/9x + 7
#6: y = -x - 6
#7: y = 2x + 5
#8: y = -4x + 7
Hope this helps! :)
Answer: x=-9/2
Alternative Form: x= -4 1/2, x= -4.5
Remark
It is easier in this case to state the irrational ones and then talk about the rationals.
sqrt(2) * sqrt(3) is irrational. The square root of 6 fills your calculator's window with many numbers and there is no pattern to them. Sqrt(6) cannot be expressed as a fraction or a repeating decimal which is also a fraction.
The last one is also irrational for the same reason. 3*pi cannot be expressed as either a repeating decimal or a fraction.
All the others are rational. The one you might have trouble with is the first one.
0.12 repeating is actually found by letting x = 0.12121212121212121212...Then
100 x = 12.121212121212121212 ...
<u> x = 0.121212121212121212..</u>. Subtract
99 x = 12
x = 12/99
So the mixed fraction you get is 3 12/99 which is 309/99
When you multiply that by 1.4 it does not change the fact that you still get a fraction. It turns out to be 721 / 165. The method is similar to the one used to get 12 / 99. I don't think you need to know the exact answer. You need only need to know that the first one is rational.
Choice 2 is rational because 9 and 25 are perfect squares. sqrt(9) = 3
Sqrt(25) = 5.
3*5 = 15.
Answer
One Two are four are all rational.
