Question 938693
5.)Find an equation of the line that passes through the two given points.
 Write the equation in slope-intercept form, if possible
passes through (1, 8) and (−2, −1);
:
The slope formula: m = {{{(y2-y1)/(x2-x1)}}}, where:
x1=1 y1=8
x2=-2 y2=-1
:
m = {{{(-1-8)/(-2-1)}}} = {{{(-9)/(-3)}}} = +3 is the slope
The slope intercept form y = mx + b
Use x1 and y1 to find b
8 = 3(1) + b
8 - 3 = b
5 = b
the equation
y = 3x + 5
:
:
:
6.)An automated production line uses distilled water at a rate of 300 gallons every 2 hours to make shampoo.
  300/2 = 150 gal/hr, this is the slope
 After the line had run for 7 hours, planners noted that 2,500 gallons of distilled water remained in the storage tank.
   t = 7; g = 2500
 Write a linear equation relating the time t in hours since the production line began and the number of gallons g of distilled water in the storage tank.
   b = original amt of distilled water (t=0)
 Write the equation in slope-intercept form. y = mx+b
2500 = -150(7) + b
2500 = -1050 + b
2500  + 1050 = b
b = 3550
the equation
g =  -150t + 3550