Slope and units

Question

Find the slope and units for the slope for:

 

time (months)                      Money(dollars)

 

5                                          1,950

15                                         2,100

 

slope:

 

units of slope:

Answer 1

We have two points on the line:

 

(5 months, $1,950) and (15 months, $2,100)

 

Slope = ($2,100 - $1,950)(15 months - 5 months) = ($150)/10 months) = $15/month

 

 

Answer 2

The formula for slope is Δy/Δx  or the CHANGE in y / CHANGE in x. That means find the DIFFERENCE (subtraction) of your y values, and find the DIFFERENCE in your x values and put them into the form y/x.  In you're problem there isn't enough information to know which, time or money, is supposed to by x and which is y, and if you put them in the wrong place your answer could be completely incorrect.

 

I'm going to ASSUME that money is your y, because usually the more time you spend doing something the more money you "use". So that would mean that your Ordered Pairs would be (5,1950) and (15,2100)

 

RECALL an OP looks like: (x,y) so x₁=15 y₁=2100 x₂=5 and y₂=1950

 

Change in y=> y₁-y₂=> 2100-1950=150

Change in x=> x₁-x₂=>15-5=10

 

NOW Δy/Δx => 150/10=15=m=>SLOPE

 

Units: $15/Month

Answer 3

Hi Wendy;

I am assuming that time is the x-axis, and that money is the y-axis.  The question is how many dollars per month are being spent.  Two points are provided.  You will proceed as if it is any other type of line.

slope=m=(y₂-y₁)/(x₂-x₁)

m=(2100-1950)/(15-5)

m=150/10

m=15

 

y=15x+b

 

b is the y-intercept, the y coordinate when x=0.

 

Let's plug-in one set of coordinates, (15, 2100)...

2100=15(15)+b

2100=225+b

1875=b

 

Let's plug-in the other set and see if the results match, (5, 1950)...

1950=15(5)+b

1950=75+b

1875=b

 

y=15x+1875

 

When $1875 dollars are at issue, no time has elapsed.  My guess is that this is the beginning balance.  Then, as every $15 is spent, a unit of time has passed.