Question 87678
If {{{f(0)=10}}} this means we have a point (0,10). If {{{f(10)=14}}} this means we have a point (10,14). So we can find the equation of the line through the two points



*[invoke calculating_slope 0, 10, 10, 14]


So now we have the equation


{{{y=(2/5)x+10}}}


which means {{{f(x)=(2/5)x+10}}}


Lets now find {{{f(5)}}} 


{{{f(5)=(2/5)(5)+10}}} Plug in {{{x=5}}}


{{{f(5)=(10/5)+10}}} Multiply


{{{f(5)=2+10}}} Reduce


{{{f(5)=12}}} Add


So {{{f(5)=12}}}



Lets now find {{{f(-5)}}} 


{{{f(-5)=(2/5)(-5)+10}}} Plug in {{{x=-5}}}


{{{f(-5)=(-10/5)+10}}} Multiply


{{{f(-5)=-2+10}}} Reduce


{{{f(-5)=8}}} Add


So {{{f(-5)=8}}}


Notice if we graph {{{y=(2/5)x+10}}} we get:



{{{drawing( 500, 500, -8, 12, -5, 15,
 graph( 500, 500, -8, 12, -5, 15, (2/5)x+10),
circle(0,10,0.05),
circle(0,10,0.08), 
circle(10,14,0.05),
circle(10,14,0.08),
circle(5,12,0.05),
circle(5,12,0.08),
circle(-5,8,0.05),
circle(-5,8,0.08)
)}}}graph of {{{y=(2/5)x+10}}} which goes through the points (0,10),(10,14),(5,12),(-5,8)


Notice how the line goes through all of the points. This verifies our answer.