17
Find y if the line through (5,3) and (-3, y) has a slope m = -
If <em>f(x)</em> is a linear function, then
<em>f(x)</em> = <em>ax</em> + <em>b</em>
for some constants <em>a</em> and <em>b</em>.
Given that <em>f</em> (1) = 4 and <em>f</em> (4) = 1, these constants are such that
<em>f</em> (1) = <em>a</em> + <em>b</em> = 4
<em>f</em> (4) = 4<em>a</em> + <em>b</em> = 1
Solve for <em>a</em> and <em>b</em> : eliminate <em>b</em> by subtracting the two equations,
(<em>a</em> + <em>b</em>) - (4<em>a</em> + <em>b</em>) = 4 - 1
-3<em>a</em> = 3
<em>a</em> = -1
Then
-1 + <em>b</em> = 4
<em>b</em> = 5
So we have
<em>f(x)</em> = -<em>x</em> + 5
Okay, so if it leaks out a pint every hour, and a gallon is 8 pints, it will take 8 hours to leak out 1 gallon. Since there are 24 hours in a day, it would leak out 3 gallons every day. Now, assuming the month we are talking about is 31 days, then we multiply 31 with 3, giving us 93 gallons in a month.
Do you need help with the third too?
