22)
x is in days and y is in gal.
(x, y) = (2 , 56) , (3, 44) Using any 2 points.
Slope = Change in y / Change in x.
Slope, m = ( 44 - 56) / (3 - 2) = -12/1 = -12 gal/day
Using: y = mx + c and using point (2 , 56) x = 2, y = 56
56 = -12*2 + c
56 = -24 + c
56 + 24 = c
80 = c
c = 80
So equation: y = mx + c
y = -12x + 80 Note: y is in gal and x is in days.
The slope -12 gals/day is the rate at which the paint is used up.
The vertical intercept, 80 gals, is the volume of paint at time, x = 0. This is the original volume of paint before painting commenced.
You notice that as the time increased, the volume of paint left reduced.
23)
x is in days and y is in gal.
(x, y) = (1 , 8.5) , (3, 25.5) Using any 2 points.
Slope = Change in y / Change in x.
Slope, m = ( 25.5 - 8.5) / (3 - 1) = 17/2 = 8.5 $/hour
Using: y = mx + c and using point (1 , 8.5) x = 1, y = 8.5
8.5 = 8.5*1 + c
8.5 = 8.5 + c
8.5 - 8.5 = c
0 = c
c = 0
So equation: y = mx + c
y = 8.5x + 0
y = 8.5x Note: y is in $ and x is in hour.
The slope 12 $/hour is the cost of carrying out the job in 1 hour.
The vertical intercept is 0. This means that at 0 hour of time, the cost of the job is $0.
Hope this explains it.