How are ratios, unit rates, and proportions related to slope intercept? last question! wil give extra points to who answers first!

Solution:

Slope intercept form of line

y= m x + c,

If you put , c=0, the equation of line in two dimensions becomes the equation of line passing through Origin .There will be infinite number of lines for different values of m, which is slope.

So, if you will write general equation of line passing through origin:

y = m x

Now coming to ratios, Suppose we have to find the value of 8: 4 , it gives a finite value, , so if we have to find The value of , a: b, then or , a = bk, which is equation of line if you replace b By x and a by y and k is used to represent Slope of line.

Similarly, While calculating Unit rate , we divide Distance by time or Displacement by time Taken . For example ,Representing Displacement or Distance by D and time taken by T, then We can write or can be Represented as , D= R T, which is same as equation of line if you replace D by y and T by x, as R will work as slope.

Considering Proportions, Four quantities a:b::c:d are said to be in proportion if , the two ratios are equivalent  that is  .If we Write either equal to t. the ratio will become , a= b t or c = d t, which is same as equation of line y=m x, if we replace b or d by x and a or c by y and t works as slope of line.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

step-by-step explanation:

what grade level is this? need to know so i can look in my old textbooks!