60 gal tank of water is leaking, with 57 gal left after 10 min, 54 gal left after 20 min. Find the slope of the line/ write the linear equation for # of gal left in tank after x amount of min.

Question

60 gal tank of water is leaking, with 57 gal left after 10 min, 54 gal left after 20 min.  Find the slope of the line/ write the linear equation for # of gal left in tank after x amount of min.

hero · Answer

Hint: 

$$(x_1, y_1) = (10, 57)$$$$(x_2,y_2) = (20,54)$$

Find the slope m, using the slope formula

Then use the point slope formula:

$$y - y_1 = m(x - x_1)$$ 

Afterwards, place the equation of the line in the form

y = mx + b

anonymous · Answer

slope is -.3?

hero · Answer

How did you get that?

anonymous · Answer

54-57/20-10

hero · Answer

I see. Okay. People normally write the slope in the form of a fraction. Good job so far.

anonymous · Answer

ok, so Y=-3/10 (10) +b?

anonymous · Answer

can you write out the equation? I am getting confused..

hero · Answer

You have to input the y value as well along with the x value if you want to find b

anonymous · Answer

y-57=-3/10(x-10)?

hero · Answer

You could do it that way as well. I'm used to using the point slope formula so I would do it that way, however, doing it your way may be easier. 

If you begin with y = mx+b and you have found the slope, then you could input the point and the slope into that formula and then solve for b: 

We know that the slope is m = -.3 and one of the points is (x,y) = (10,57). So to find the b value, y = mx + b becomes: 

57 = .3(10) + b

Can you finish up here by solving for b?

hero · Answer

No matter which method you use, you should end up with the same answer in the form y = mx + b. Using your method, once you find b, you would rewrite the slope-intercept formula, but include the values for m and b only.

anonymous · Answer

I think I may have forgotten a rule here. Why does -.3 become .3?