SOLUTION: 5.7 point-slope lab 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) an

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Question 938693: 5.7 point-slope lab
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)
6.)An automated production line uses distilled water at a rate of 300 gallons every 2 hours to make shampoo. After the line had run for 7 hours, planners noted that 2,500 gallons of distilled water remained in the storage tank. 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. Write the equation in slope-intercept form.

Answer by ankor@dixie-net.com(22740) (Show Source):
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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 = , where:
x1=1 y1=8
x2=-2 y2=-1
:
m = = = +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