Question 441613
Write an equation that satisfies the given conditions: f(0)=12,f(3)=-2
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That's the same as this problem:

Write the equation of the line that passes through the points
(0,12) and (3,-2), then change the y to f(x).

Use the slope formula:

{{{m = (y[2]-y[1])/(x[2]-x[1]) = (-2-12)/(3-0) = -14/3}}}

Then use the point-slope formula:

{{{y-y[1]=m(x-x[1])}}}

{{{y-12=expr(-14/3)(x-0)}}}

{{{y-12=expr(-14/3)x}}}

{{{y=expr(-14/3)x+12}}}

Now write f(x) for y:

{{{f(x)=expr(-14/3)x+12}}}

-----------------------------

Checking:

{{{f(x)=expr(-14/3)x+12}}}

Substitute 0 for x

{{{f(0)=expr(-14/3)(0)+12}}}

{{{f(0)=0+12}}}

{{{f(0)=12}}}

That checks.

Substitute 3 for x

{{{f(3)=expr(-14/3)(3)+12}}}

{{{f(3)=expr(-14/cross(3))(cross(3))+12}}}

{{{f(3)=-14+12}}}

{{{f(3)=-2}}}

That checks, so we're right.

Edwin</pre>